HP 39gs graphing calculator
user's guide
Edition3
Part Number F2223AA-90001
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Contents
Preface
Manual conventions ..............................................................P-1
Notice .................................................................................P-2
1 Getting started
On/off, cancel operations......................................................1-1
The display ..........................................................................1-2
The keyboard .......................................................................1-3
Menus .................................................................................1-8
Input forms ...........................................................................1-9
Mode settings.....................................................................1-10
Setting a mode...............................................................1-11
Aplets (E-lessons).................................................................1-12
Aplet library ..................................................................1-16
Aplet views....................................................................1-16
Aplet view configuration..................................................1-18
Mathematical calculations....................................................1-19
Using fractions....................................................................1-25
Complex numbers ...............................................................1-29
Catalogs and editors...........................................................1-30
2 Aplets and their views
Aplet views ..........................................................................2-1
About the Symbolic view...................................................2-1
Defining an expression (Symbolic view) ..............................2-1
Evaluating expressions......................................................2-3
About the Plot view...........................................................2-5
Setting up the plot (Plot view setup).....................................2-5
Exploring the graph..........................................................2-7
Other views for scaling and splitting the graph ..................2-13
About the numeric view...................................................2-16
Setting up the table (Numeric view setup)..........................2-16
Exploring the table of numbers.........................................2-17
Building your own table of numbers..................................2-19
“Build Your Own” menu keys...........................................2-20
Example: plotting a circle ................................................2-20
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3 Function aplet
About the Function aplet........................................................ 3-1
Getting started with the Function aplet................................ 3-1
Function aplet interactive analysis........................................... 3-9
Plotting a piecewise-defined function................................ 3-12
4 Parametric aplet
About the Parametric aplet .................................................... 4-1
Getting started with the Parametric aplet............................. 4-1
5 Polar aplet
Getting started with the Polar aplet ......................................... 5-1
6 Sequence aplet
About the Sequence aplet...................................................... 6-1
Getting started with the Sequence aplet.............................. 6-1
7 Solve aplet
About the Solve aplet............................................................ 7-1
Getting started with the Solve aplet.................................... 7-2
Use an initial guess............................................................... 7-5
Interpreting results ................................................................ 7-6
Plotting to find guesses.......................................................... 7-7
Using variables in equations................................................ 7-10
8 Linear Solver aplet
About the Linear Solver aplet ................................................. 8-1
Getting started with the Linear Solver aplet.......................... 8-1
9 Triangle Solve aplet
About the Triangle Solver aplet .............................................. 9-1
Getting started with the Triangle Solver aplet....................... 9-1
10 Statistics aplet
About the Statistics aplet...................................................... 10-1
Getting started with the Statistics aplet.............................. 10-1
Entering and editing statistical data ...................................... 10-6
Defining a regression model.......................................... 10-12
Computed statistics........................................................... 10-14
Plotting............................................................................ 10-15
Plot types .................................................................... 10-16
Fitting a curve to 2VAR data ......................................... 10-17
Setting up the plot (Plot setup view) ................................ 10-18
Trouble-shooting a plot ................................................. 10-19
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Exploring the graph......................................................10-19
Calculating predicted values..........................................10-20
11 Inference aplet
About the Inference aplet .....................................................11-1
Getting started with the Inference aplet .............................11-1
Importing sample statistics from the Statistics aplet..............11-4
Hypothesis tests ..................................................................11-8
One-Sample Z-Test..........................................................11-8
Two-Sample Z-Test..........................................................11-9
One-Proportion Z-Test....................................................11-10
Two-Proportion Z-Test....................................................11-11
One-Sample T-Test........................................................11-12
Two-Sample T-Test ........................................................11-14
Confidence intervals..........................................................11-15
One-Sample Z-Interval...................................................11-15
Two-Sample Z-Interval ...................................................11-16
One-Proportion Z-Interval...............................................11-17
Two-Proportion Z-Interval ...............................................11-17
One-Sample T-Interval ...................................................11-18
Two-Sample T-Interval....................................................11-19
12 Using the Finance Solver
Background........................................................................12-1
Performing TVM calculations ................................................12-4
Calculating Amortizations................................................12-7
13 Using mathematical functions
Math functions....................................................................13-1
The MATH menu ............................................................13-1
Math functions by category ..................................................13-2
Keyboard functions.........................................................13-3
Calculus functions...........................................................13-6
Complex number functions...............................................13-7
Constants ......................................................................13-8
Conversions...................................................................13-8
Hyperbolic trigonometry..................................................13-9
List functions ................................................................13-10
Loop functions..............................................................13-10
Matrix functions ...........................................................13-11
Polynomial functions .....................................................13-11
Probability functions......................................................13-12
Real-number functions ...................................................13-13
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Two-variable statistics................................................... 13-17
Symbolic functions ....................................................... 13-17
Test functions............................................................... 13-18
Trigonometry functions.................................................. 13-19
Symbolic calculations........................................................ 13-20
Finding derivatives....................................................... 13-21
Program constants and physical constants ........................... 13-24
Program constants........................................................ 13-24
Physical constants ........................................................ 13-25
14 Variables and memory management
Introduction ....................................................................... 14-1
Storing and recalling variables............................................. 14-2
The VARS menu.................................................................. 14-4
Memory Manager .............................................................. 14-9
15 Matrices
Introduction ....................................................................... 15-1
Creating and storing matrices .............................................. 15-2
Working with matrices........................................................ 15-4
Matrix arithmetic ................................................................ 15-6
Solving systems of linear equations .................................. 15-8
Matrix functions and commands......................................... 15-10
Argument conventions .................................................. 15-10
Matrix functions........................................................... 15-10
Examples......................................................................... 15-13
16 Lists
Displaying and editing lists.................................................. 16-4
Deleting lists.................................................................. 16-6
Transmitting lists............................................................. 16-6
List functions....................................................................... 16-6
Finding statistical values for list elements................................ 16-9
17 Notes and sketches
Introduction ....................................................................... 17-1
Aplet note view.................................................................. 17-1
Aplet sketch view................................................................ 17-3
The notepad ...................................................................... 17-6
18 Programming
Introduction ....................................................................... 18-1
Program catalog............................................................ 18-2
Creating and editing programs ............................................ 18-4
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Using programs ..................................................................18-7
Customizing an aplet...........................................................18-9
Aplet naming convention...............................................18-10
Example......................................................................18-10
Programming commands....................................................18-13
Aplet commands ..........................................................18-14
Branch commands........................................................18-17
Drawing commands......................................................18-19
Graphic commands ......................................................18-21
Loop commands...........................................................18-23
Matrix commands.........................................................18-24
Print commands............................................................18-26
Prompt commands........................................................18-26
Stat-One and Stat-Two commands ..................................18-30
Stat-Two commands......................................................18-30
Storing and retrieving variables in programs....................18-31
Plot-view variables........................................................18-32
Symbolic-view variables ................................................18-39
Numeric-view variables.................................................18-41
Note variables .............................................................18-44
Sketch variables...........................................................18-44
19 Extending aplets
Creating new aplets based on existing aplets .........................19-1
Using a customized aplet ................................................19-3
Resetting an aplet................................................................19-3
Annotating an aplet with notes .............................................19-4
Annotating an aplet with sketches .........................................19-4
Downloading e-lessons from the web.....................................19-4
Sending and receiving aplets ...............................................19-4
Sorting items in the aplet library menu list ..............................19-6
Reference information
Glossary..............................................................................R-1
Resetting the HP 39gs............................................................R-3
To erase all memory and reset defaults................................R-3
If the calculator does not turn on.........................................R-4
Operating details..................................................................R-4
Batteries..........................................................................R-4
Variables .............................................................................R-6
Home variables................................................................R-6
Function aplet variables.....................................................R-7
Parametric aplet variables .................................................R-8
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Polar aplet variables ........................................................ R-9
Sequence aplet variables................................................ R-10
Solve aplet variables...................................................... R-11
Statistics aplet variables.................................................. R-12
MATH menu categories....................................................... R-13
Math functions............................................................... R-13
Program constants.......................................................... R-15
Physical Constants ......................................................... R-16
Program commands ....................................................... R-17
Status messages ................................................................. R-18
Limited Warranty
Service ..........................................................................W-3
Regulatory information.....................................................W-5
Index
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Preface
The HP 39gs is a feature-rich graphing calculator. It is
also a powerful mathematics learning tool. The HP 39gs
is designed so that you can use it to explore mathematical
functions and their properties.
You can get more information on the HP 39gs from
Hewlett-Packard’s Calculators web site. You can
download customized aplets from the web site and load
them onto your calculator. Customized aplets are special
applications developed to perform certain functions, and
to demonstrate mathematical concepts.
Hewlett Packard’s Calculators web site can be found at:
http://www.hp.com/calculators
Manual conventions
The following conventions are used in this manual to
represent the keys that you press and the menu options
that you choose to perform the described operations.
•
Key presses are represented as follows:
, etc.
,
,
•
Shift keys, that is the key functions that you access by
pressing the
follows:
key first, are represented as
ACOS, etc.
CLEAR,
MODES,
•
•
Numbers and letters are represented normally, as
follows:
5, 7, A, B, etc.
Menu options, that is, the functions that you select
using the menu keys at the top of the keypad are
represented as follows:
,
,
.
•
•
Input form fields and choose list items are represented
as follows:
Function, Polar, Parametric
Your entries as they appear on the command line or
within input forms are represented as follows:
2
2*X -3X+5
P-1
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Notice
This manual and any examples contained herein are
provided as-is and are subject to change without notice.
Except to the extent prohibited by law, Hewlett-Packard
Company makes no express or implied warranty of any
kind with regard to this manual and specifically disclaims
the implied warranties and conditions of merchantability
and fitness for a particular purpose and Hewlett-Packard
Company shall not be liable for any errors or for
incidental or consequential damage in connection with
the furnishing, performance or use of this manual and the
examples herein.
© 1994–1995, 1999–2000, 2003–2006 Hewlett-
Packard Development Company, L.P.
The programs that control your HP 39gs are copyrighted
and all rights are reserved. Reproduction, adaptation, or
translation of those programs without prior written
permission from Hewlett-Packard Company is also
prohibited.
P-2
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1
Getting started
On/off, cancel operations
To turn on
Press
to turn on the calculator.
To cancel
When the calculator is on, the
current operation.
key cancels the
To turn off
Press
OFF to turn the calculator off.
To save power, the calculator turns itself off after several
minutes of inactivity. All stored and displayed information
is saved.
If you see the ((•)) annunciator or the Low Batmessage,
then the calculator needs fresh batteries.
HOME
HOME is the calculator’s home view and is common to all
aplets. If you want to perform calculations, or you want to
quit the current activity (such as an aplet, a program, or
an editor), press
. All mathematical functions are
available in the HOME. The name of the current aplet is
displayed in the title of the home view.
Protective cover
The calculator is provided with a slide cover to protect the
display and keyboard. Remove the cover by grasping
both sides of it and pulling down.
You can reverse the slide cover and slide it onto the back
of the calculator. this will help prevent you losing the
cover while you are using the calculator.
To prolong the life of the calculator, always place the
cover over the display and keyboard when you are not
using the calculator.
Getting started
1-1
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The display
To adjust the
contrast
Simultaneously press
decrease) the contrast.
and
(or
) to increase (or
To clear the display
•
•
Press CANCEL to clear the edit line.
Press
CLEAR to clear the edit line and the
display history.
Parts of the
display
Title
History
Edit line
Menu key
labels
Menu key or soft key labels. The labels for the menu
keys’ current meanings.
menu key in this picture. “Press
is the label for the first
” means to press the
first menu key, that is, the leftmost top-row key on the
calculator keyboard.
Edit line. The line of current entry.
History. The HOME display (
) shows up to four
lines of history: the most recent input and output. Older
lines scroll off the top of the display but are retained in
memory.
Title. The name of the current aplet is displayed at the top
of the HOME view. RAD, GRD, DEG specify whether
Radians, Grads or Degrees angle mode is set for HOME.
The ꢀ and ꢁ symbols indicate whether there is more
history in the HOME display. Press the
scroll in the HOME display.
and
to
N O T E
This user’s guide contains images from the HP 39gs and
does not display the menu key label.
1-2
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Annunciators. Annunciators are symbols that appear
above the title bar and give you important status
information.
Annunciator
Description
Shift in effect for next keystroke.
To cancel, press
again.
α
Alpha in effect for next keystroke.
To cancel, press
Low battery power.
Busy.
again.
((•))
Data is being transferred via
infrared or cable.
The keyboard
Menu keys
HP 39gs
Graphing Calculator
Menu Key
Labels
Menu Keys
Cursor
Keys
Aplet Control
Keys
Alpha Key
Shift Key
Enter
Key
Getting started
1-3
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•
•
On the calculator keyboard, the top row of keys are
called menu keys. Their meanings depend on the
context—that’s why their tops are blank. The menu
keys are sometimes called “soft keys”.
The bottom line of the display shows the labels for the
menu keys’ current meanings.
Aplet control keys
The aplet control keys are:
Key
Meaning
Displays the Symbolic view for the
current aplet. See “Symbolic view”
on page 1-16.
Displays the Plot view for the current
aplet. See “Plot view” on page 1-16.
Displays the Numeric view for the
current aplet. See “Numeric view” on
page 1-17.
Displays the HOME view. See
“HOME” on page 1-1.
Displays the Aplet Library menu. See
“Aplet library” on page 1-16.
Displays the VIEWS menu. See
“Aplet views” on page 1-16.
1-4
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Entry/Edit keys
The entry and edit keys are:
Key
Meaning
Cancels the current operation if the
(CANCEL)
calculator is on by pressing
.
Pressing
, then OFF turns the
calculator off.
Accesses the function printed in blue
above a key.
Returns to the HOME view, for
performing calculations.
Accesses the alphabetical
characters printed in orange below
a key. Hold down to enter a string
of characters.
Enters an input or executes an
operation. In calculations,
acts like “=”. When
or
is present as a menu key,
acts the same as pressing
.
or
Enters a negative number. To enter
–25, press
25. Note: this is not
the same operation that the subtract
button performs ( ).
Enters the independent variable by
inserting X, T, θ, or N into the edit
line, depending on the current
active aplet.
Deletes the character under the
cursor. Acts as a backspace key if
the cursor is at the end of the line.
Clears all data on the screen. On a
settings screen, for example Plot
CLEAR
Setup,
CLEAR returns all
settings to their default values.
Moves the cursor around the
,
,
,
display. Press
first to move to
the beginning, end, top or bottom.
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Key
Meaning (Continued)
CHARS
Displays a menu of all available
characters. To type one, use the
arrow keys to highlight it, and press
. To select multiple characters,
select each and press
press
, then
.
Shifted keystrokes
There are two shift keys that you use to access the
operations and characters printed above the keys:
and
.
Key
Description
Press the
key to access the
operations printed in blue above the
keys. For instance, to access the
Modes screen, press
, then
press
. (MODES is labeled in
blue above the
not need to hold down
key). You do
when
you press HOME. This action is
depicted in this manual as “press
MODES.”
To cancel a shift, press
again.
The alphabetic keys are also shifted
keystrokes. For instance, to type Z,
press
Z. (The letters are
printed in orange to the lower right of
each key.)
To cancel Alpha, press
again.
For a lower case letter, press
.
For a string of letters, hold down
while typing.
1-6
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HELPWITH
Example
The HP 39gs built-in help is available in HOME only. It
provides syntax help for built-in math functions.
Access the HELPWITH command by pressing
SYNTAX and then the math key for which you require
syntax help.
Press
SYNTAX
Note: Remove the left parenthesis from built-in
functions such as sine, cosine, and tangent before
invoking the HELPWITH command.
Math keys
HOME (
) is the place to do calculations.
Keyboard keys. The most common operations are
available from the keyboard, such as the arithmetic (like
) and trigonometric (like
to complete the operation:
displays 16.
) functions. Press
256
.
MATH menu. Press
to open the MATH
menu. The MATH menu is a
comprehensive list of math
functions that do not appear
on the keyboard. It also
includes categories for all other functions and constants.
The functions are grouped by category, ranging in
alphabetical order from Calculus to Trigonometry.
•
The arrow keys scroll through the list (
and move from the category list in the left column
to the item list in the right column ( ).
,
)
,
•
•
•
Press
to insert the selected command onto the
edit line.
Press
to dismiss the MATH menu without
selecting a command.
Pressing
displays the list of Program
Constants. You can use these in programs that
you develop.
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1-7
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•
•
Pressing
displays a menu of physical
constants from the fields of chemistry, physics,
and quantum mechanics. You can use these
constants in calculations. (See “Physical
constants” on page 13-25 for more information.)
Pressing
takes you to the beginning of the
MATH menu.
See “Math functions by category” on page 13-2 for
details of the math functions.
H I N T
When using the MATH menu, or any menu on the
hp 39gs, pressing an alpha key takes you straight to the
first menu option beginning with that alpha character.
With this method, you do not need to press
first.
Just press the key that corresponds to the command’s
beginning alpha character.
Program
commands
Pressing
CMDS displays the list of Program
Commands. See “Programming commands” on
page 18-13.
Inactive keys
If you press a key that does not operate in the current
context, a warning symbol like this
no beep.
appears. There is
!
Menus
A menu offers you a choice
of items. Menus are
displayed in one or two
columns.
•
The
arrow in the
display means more
items below.
•
•
The
arrow in the
display means more items above.
To search a menu
Press
or
or
to scroll through the list. If you press
, you’ll go all the way to
the end or the beginning of the list. Highlight the item
you want to select, then press
(or
).
1-8
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•
If there are two columns, the left column shows
general categories and the right column shows
specific contents within a category. Highlight a
general category in the left column, then highlight an
item in the right column. The list in the right column
changes when a different category is highlighted.
Press
or
when you have highlighted your
selection.
•
•
To speed-search a list, type the first letter of the word.
For example, to find the Matrix category in
press , the Alpha “M” key.
,
To go up a page, you can press
down a page, press
. To go
.
To cancel a menu
Press
(for CANCEL) or
. This cancels the
current operation.
Input forms
An input form shows several fields of information for you
to examine and specify. After highlighting the field to
edit, you can enter or edit a number (or expression). You
can also select options from a list (
forms include items to check (
examples input forms.
). Some input
). See below for
Reset input form
values
To reset a field to its default values in an input form, move
the cursor to that field and press
. To reset all default
field values in the input form, press
CLEAR.
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Mode settings
You use the Modes input form to set the modes for HOME.
H I N T
Although the numeric setting in Modes affects only
HOME, the angle setting controls HOME and the current
aplet. The angle setting selected in Modes is the angle
setting used in both HOME and current aplet. To further
configure an aplet, you use the SETUP keys (
and
).
Press
form.
MODES to access the HOME MODES input
Setting
Options
Angle
Measure
Angle values are:
Degrees. 360 degrees in a circle.
Radians. 2π radians in a circle.
Grads. 400 grads in a circle.
The angle mode you set is the angle
setting used in both HOME and the
current aplet. This is done to ensure
that trigonometric calculations done in
the current aplet and HOME give the
same result.
Number
Format
The number format mode you set is the
number format used in both HOME
and the current aplet.
Standard. Full-precision display.
Fixed. Displays results rounded to a
number of decimal places. Example:
123.456789 becomes 123.46 in
Fixed 2 format.
Scientific. Displays results with an
exponent, one digit to the left of the
decimal point, and the specified
number of decimal places. Example:
123.456789 becomes 1.23E2 in
Scientific 2 format.
1-10
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Setting
Options (Continued)
Engineering. Displays result with an
exponent that is a multiple of 3, and
the specified number of significant
digits beyond the first one. Example:
123.456E7 becomes 1.23E9 in
Engineering 2 format.
Fraction. Displays results as fractions
based on the specified number of
decimal places. Examples:
123.456789 becomes 123 in
Fraction 2 format, and .333 becomes
1/3 and 0.142857 becomes 1/7.
See “Using fractions” on page 1-25.
Mixed Fraction. Displays results as
mixed fractions based on the specified
number of decimal places. A mixed
fraction has an integer part and a
fractional part. Examples:
123.456789 becomes 123+16/35
in Fraction 2 format, and 7÷ 3 returns
2+1/3. See “Using fractions” on
page 1-25.
Decimal
Mark
Dot or Comma. Displays a number
as 12456.98 (Dot mode) or as
12456,98 (Comma mode). Dot mode
uses commas to separate elements in
lists and matrices, and to separate
function arguments. Comma mode
uses periods (dot) as separators in
these contexts.
Setting a mode
This example demonstrates how to change the angle
measure from the default mode, radians, to degrees for
the current aplet. The procedure is the same for changing
number format and decimal mark modes.
1. Press
form.
MODES to open the HOME MODES input
Getting started
1-11
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The cursor (highlight) is
in the first field, Angle
Measure.
2. Press
to display a
list of choices.
3. Press
to select
Degrees,and press
. The angle measure
changes to degrees.
4. Press
HOME.
to return to
H I N T
Whenever an input form has a list of choices for a field,
you can press
to cycle through them instead of using
.
Aplets (E-lessons)
Aplets are the application environments where you
explore different classes of mathematical operations. You
select the aplet that you want to work with.
Aplets come from a variety of sources:
•
•
Aplets created by saving existing aplets, which have
been modified, with specific configurations. See
“Creating new aplets based on existing aplets” on
page 19-1.
•
•
Downloaded from HP’s Calculators web site.
Copied from another calculator.
Aplets are stored in the Aplet
library. See “Aplet library”
on page 1-16 for further
information.
You can modify
configuration settings for the graphical, tabular, and
1-12
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symbolic views of the aplets in the following table. See
“Aplet view configuration” on page 1-18 for further
information.
Aplet
name
Use this aplet to explore:
Function
Real-valued, rectangular functions y in
terms of x. Example: y = 2x2 + 3x + 5 .
Inference
Confidence intervals and Hypothesis
tests based on the Normal and
Students-t distributions.
Parametric Parametric relations x and y in terms of
t. Example: x = cos(t) and y = sin(t).
Polar
Polar functions r in terms of an angle θ.
Example: r = 2cos(4θ) .
Sequence
Sequence functions U in terms of n, or
in terms of previous terms in the same or
another sequence, such as Un – 1 and
Un – 2 . Example: U1 = 0 , U2 = 1
and Un = Un – 2 + Un – 1
.
Solve
Equations in one or more real-valued
variables. Example: x + 1 = x2 – x – 2 .
Finance
Time Value of Money (TVM)
calculations.
Linear
Solver
Solutions to sets of two or three linear
equations.
Triangle
Solver
Unknown values for the lengths and
angles of triangles.
Statistics
One-variable (x) or two-variable (x and
y) statistical data.
In addition to these aplets, which can be used in a variety
of applications, the HP 39gs is supplied with two
teaching aplets: Quad Explorer and Trig Explorer. You
cannot modify configuration settings for these aplets.
A great many more teaching aplets can be found at HP’s
web site and other web sites created by educators,
together with accompanying documentation, often with
student work sheets. These can be downloaded free of
Getting started
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1-13
charge and transferred to the HP 39gs using the provided
Connectivity Kit.
Quad Explorer
aplet
The Quad Explorer aplet is used to investigate the
behaviour of y = a(x + h)2 + v as the values of a, h and
v change, both by manipulating the equation and seeing
the change in the graph, and by manipulating the graph
and seeing the change in the equation.
H I N T
More detailed documentation, and an accompanying
student work sheet can be found at HP’s web site.
Press
, select Quad
Explorer, and then press
. The Quad Explorer
aplet opens in
mode, in which the arrow
keys, the
and the
and
keys,
key are used to change the shape of the
graph. This changing shape is reflected in the equation
displayed at the top right corner of the screen, while the
original graph is retained for comparison. In this mode
the graph controls the equation.
It is also possible to have the
equation control the graph.
Pressing
displays a
sub-expression of your
equation.
Pressing the
expressions, while pressing the
their values.
and
key moves between sub-
and
key changes
Pressing
allows the user to select whether all three
sub-expressions will be explored at once or only one at a
time.
A
button is provided to
evaluate the student’s
knowledge. Pressing
displays a target quadratic
graph. The student must
manipulate the equation’s parameters to make the
equation match the target graph. When a student feels
that they have correctly chosen the parameters a
button evaluates the answer and provide feedback. An
button is provided for those who give up!
1-14
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Trig Explorer aplet
The Trig Explorer aplet is used to investigate the
behaviour of the graph of y = asin(bx + c) + d as the
values of a, b, c and d change, both by manipulating the
equation and seeing the change in the graph, or by
manipulating the graph and seeing the change in the
equation.
Press
, select Trig
Explorer, and then press
to display the screen
shown right.
In this mode, the graph
controls the equation.
Pressing the
keys transforms the
graph, with these
transformations reflected in the equation.
and
The button labelled
a toggle between
is
Origin
and
is chosen, the ‘point of
control’ is at the origin (0,0)
and the and
keys control vertical and
horizontal transformations. When
. When
is chosen the
‘point of control’ is on the first extremum of the graph (i.e.
for the sine graph at (π ⁄ 2,1) .
The arrow keys change the
Extremum
amplitude and frequency of
the graph. This is most easily
seen by experimenting.
Pressing
displays the
equation at the top of the
screen. The equation is
controlled by the graph.
Pressing the
and
keys moves from parameter
to parameter. Pressing the
parameter’s values.
or
key changes the
The default angle setting for this aplet is radians. The
angle setting can be changed to degrees by pressing
.
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Aplet library
Aplets are stored in the Aplet library.
To open an aplet
Press
aplet and press
to display the Aplet library menu. Select the
or
.
From within an aplet, you can return to HOME any time
by pressing
.
Aplet views
When you have configured an aplet to define the relation
or data that you want to explore, you can display it in
different views. Here are illustrations of the three major
aplet views (Symbolic, Plot, and Numeric), the six
supporting aplet views (from the VIEWS menu), and the
two user-defined views (Note and Sketch).
Note: some aplets—such as the Linear Solver aplet and
the Triangle Solver aplet—only have a single view, the
Numeric view.
Symbolic view
Plot view
Press
to display the aplet’s Symbolic view.
You use this view to define
the function(s) or equation(s)
that you want to explore.
See “About the Symbolic
view” on page 2-1 for
further information.
Press
to display the aplet’s Plot view.
In this view, the functions that
you have defined are
displayed graphically.
See “About the Plot view” on
page 2-5 for further
information.
1-16
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Numeric view
Press
to display the aplet’s Numeric view.
In this view, the functions that
you have defined are
displayed in tabular format.
See “About the numeric
view” on page 2-16 for
further information.
Plot-Table view
The VIEWS menu contains the Plot-Table view.
Select Plot-Table
Splits the screen into the plot
and the data table. See
“Other views for scaling and
splitting the graph” on
page 2-13 for futher information.
Plot-Detail view
The VIEWS menu contains the Plot-Detail view.
Select Plot-Detail
Splits the screen into the plot
and a close-up.
See “Other views for scaling and splitting the graph” on
page 2-13 for further information.
Overlay Plot
view
The VIEWS menu contains the Overlay Plot view.
Select Overlay Plot
Plots the current
expression(s)withouterasing
any pre-existing plot(s).
See “Other views for scaling and splitting the graph” on
page 2-13 for further information.
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Note view
Press
NOTE to display the aplet’s note view.
This note is transferred with
the aplet if it is sent to
another calculator or to a
PC. A note view contains text
to supplement an aplet.
See “Notes and sketches” on page 17-1 for further
information.
Sketch view
Press
SKETCH to display the aplet’s sketch view.
Displays pictures to
supplement an aplet.
See “Notes and sketches” on
page 17-1 for further
information.
Aplet view configuration
You use the SETUP keys (
, and
) to configure the aplet. For example, press
SETUP-PLOT (
) to display the input form for
setting the aplet’s plot settings. Angle measure is
controlled using the MODES view.
Plot Setup
Press
SETUP-PLOT.
Sets parameters to plot a
graph.
Numeric Setup
Symbolic Setup
Press
SETUP-NUM. Sets
parameters for building a
table of numeric values.
This view is only available in
the Statistics aplet in
mode, where it plays an
important role in choosing
data models.
Press
SETUP-SYMB.
1-18
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To change views
select a different view by pressing
keys or select a view from the VIEWS menu. To change
to HOME, press . You do not explicitly close the
,
,
current view, you just enter another one—like passing
from one room into another in a house. Data that you
enter is automatically saved as you enter it.
To save aplet
configuration
You can save an aplet configuration that you have used,
“Creating new aplets based on existing aplets” on
page 19-1.
Mathematical calculations
The most commonly used math operations are available
from the keyboard. Access to the rest of the math
functions is via the MATH menu ( ).
To access programming commands, press
CMDS.
See “Programming commands” on page 18-13 for
further information.
Where to start
The home base for the calculator is the HOME view
(
). You can do all calculations here, and you can
access all
operations.
Entering
expressions
•
•
Enter an expression into the HP 39gs in the same left-
to-right order that you would write the expression.
This is called algebraic entry.
To enter functions, select the key or MATH menu item
for that function. You can also enter a function by
using the Alpha keys to spell out its name.
•
Press
to evaluate the expression you have in
the edit line (where the blinking cursor is). An
expression can contain numbers, functions, and
variables.
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232 – 14 8
---------------------------
Example
Calculate
ln(45) :
–3
23
14
8
3
45
Long results
If the result is too long to fit on the display line, or if you
want to see an expression in textbook format, press
to highlight it and then press
.
Negative
numbers
Type
to start a negative number or to insert a
negative sign.
To raise a negative number to a power, enclose it in
parentheses. For example, (–5) = 25, whereas –5 =
–25.
2
2
Scientific
A number like 5 × 104 or 3.21 × 10–7 is written in
scientific notation, that is, in terms of powers of ten. This
is simpler to work with than 50000 or 0.000000321. To
enter numbers like these, use EEX. (This is easier than
notation
(powers of 10)
using
10
.)
(4 × 10–13)(6 × 1023
)
----------------------------------------------------
Example
Calculate
3 × 10–5
4
EEX
13
6
EEX
EEX
23
3
5
Explicit and
implicit
multiplication
Implied multiplication takes place when two operands
appear with no operator in between. If you enter AB, for
example, the result is A*B.
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However, for clarity, it is better to include the
multiplication sign where you expect multiplication in an
expression. It is clearest to enter ABas A*B.
H I N T
Implied multiplication will not always work as expected.
For example, entering A(B+4)will not give A*(B+4).
Instead an error message is displayed: “Invalid User
Function”. This is because the calculator interprets
A(B+4)as meaning ‘evaluate function Aat the value
B+4’, and function Adoes not exist. When in doubt, insert
the * sign manually.
Parentheses
You need to use parentheses to enclose arguments for
functions, such as SIN(45). You can omit the final
parenthesis at the end of an edit line. The calculator
inserts it automatically.
Parentheses are also important in specifying the order of
operation. Without parentheses, the HP 39gs calculates
according to the order of algebraic precedence (the next
topic). Following are some examples using parentheses.
Entering...
45
Calculates...
sin (45 + π)
sin (45) + π
85 × 9
π
45
π
85
9
85
9
85 × 9
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1-21
Algebraic
precedence
order of
Functions within an expression are evaluated in the
following order of precedence. Functions with the same
precedence are evaluated in order from left to right.
1. Expressions within parentheses. Nested parentheses
are evaluated from inner to outer.
evaluation
2. Prefix functions, such as SIN and LOG.
3. Postfix functions, such as !
4. Power function, ^, NTHROOT.
5. Negation, multiplication, and division.
6. Addition and subtraction.
7. AND and NOT.
8. OR and XOR.
9. Left argument of | (where).
10.Equals, =.
Largest and
smallest
numbers
The smallest number the HP 39gs can represent is
–499
1 × 10
(1E–499). A smaller result is displayed as
499
zero. The largest number is 9.99999999999 × 10
(1E499). A greater result is displayed as this number.
Clearing
numbers
•
clears the character under the cursor. When the
cursor is positioned after the last character,
deletes the character to the left of the cursor, that is, it
performs the same as a backspace key.
•
•
CANCEL (
) clears the edit line.
CLEAR clears all input and output in the
display, including the display history.
Using previous
results
The HOME display (
) shows you four lines of
input/output history. An unlimited (except by memory)
number of previous lines can be displayed by scrolling.
You can retrieve and reuse any of these values or
expressions.
Input
Output
Last input
Last output
Edit line
1-22
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When you highlight a previous input or result (by pressing
), the and menu labels appear.
To copy a previous
line
Highlight the line (press
) and press
. The
number (or expression) is copied into the edit line.
To reuse the last
result
Press
ANS (last answer) to put the last result from the
HOME display into an expression. ANS is a variable that
is updated each time you press
.
To repeat a
previous line
To repeat the very last line, just press
. Otherwise,
highlight the line (press
) first, and then press
.
The highlighted expression or number is re-entered. If the
previous line is an expression containing the ANS, the
calculation is repeated iteratively.
Example
See how
(50), and
ANS retrieves and reuses the last result
updates ANS (from 50 to 75 to 100).
50
25
You can use the last result as the first expression in the edit
line without pressing ANS. Pressing , or
,
,
, (or other operators that require a preceding
argument) automatically enters ANS before the operator.
You can reuse any other expression or value in the HOME
display by highlighting the expression (using the arrow
keys), then pressing
. See “Using previous results”
on page 1-22 for more details.
The variable ANS is different from the numbers in HOME’s
display history. A value in ANS is stored internally with the
full precision of the calculated result, whereas the
displayed numbers match the display mode.
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H I N T
When you retrieve a number from ANS, you obtain the
result to its full precision. When you retrieve a number
from the HOME’s display history, you obtain exactly what
was displayed.
Pressing
whereas pressing
into the edit line.
evaluates (or re-evaluates) the last input,
ANS copies the last result (as ANS)
Storing a value
in a variable
You can save an answer in a variable and use the
variable in later calculations. There are 27 variables
available for storing real values. These are A to Z and θ.
See Chapter 14, “Variables and memory management”
for more information on variables. For example:
1. Perform a calculation.
45
8
3
2. Store the result in the A variable.
A
3. Perform another calculation using the A variable.
95
2
A
1-24
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Accessing the
display history
Pressing
enables the highlight bar in the display
history. While the highlight bar is active, the following
menu and keyboard keys are very useful:
Key
Function
,
Scrolls through the display history.
Copies the highlighted expression to
the position of the cursor in the edit line.
Displays the current expression in
standard mathematical form.
Deletes the highlighted expression from
the display history, unless there is a
cursor in the edit line.
Clears all lines of display history and
the edit line.
CLEAR
Clearing the
display history
It’s a good habit to clear the display history (
CLEAR) whenever you have finished working in HOME. It
saves calculator memory to clear the display history.
Remember that all your previous inputs and results are
saved until you clear them.
Using fractions
To work with fractions in HOME, you set the number
format to Fractionor Mixed Fraction, as follows:
Setting Fraction
mode
1. In HOME, open the HOME MODES input form.
MODES
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2. Select Number Format, press
to display the
options, and highlight Fractionor Mixed
Fraction.
3. Press
to select the Number Format option, then
move to the precision value field.
4. Enter the precision value that you want to use, and
press
to HOME.
to set the precision. Press
to return
See “Setting fraction precision” below for more
information.
Setting fraction
precision
The fraction precision setting determines the precision in
which the HP 39gs converts a decimal value to a fraction.
The greater the precision value that is set, the closer the
fraction is to the decimal value.
By choosing a precision of 1 you are saying that the
fraction only has to match 0.234 to at least 1 decimal
place (3/13 is 0.23076...).
The fractions used are found using the technique of
continued fractions.
When converting recurring decimals this can be
important. For example, at precision 6 the decimal
0.6666 becomes 3333/5000 (6666/10000) whereas
at precision 3, 0.6666 becomes 2/3, which is probably
what you would want.
For example, when converting .234 to a fraction, the
precision value has the following effect:
1-26
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•
•
•
•
Precision set to 1:
Precision set to 2:
Precision set to 3:
Precision set to 4
Fraction
calculations
When entering fractions:
•
You use the
key to separate the numerator part
and the denominator part of the fraction.
1
•
To enter a mixed fraction, for example, 1 / , you
2
1
enter it in the format (1+ / ).
2
For example, to perform the following calculation:
3
7
3(2 / + 5 / )
4
8
1. Set the Number format mode to Fractionor
Mixed Fractionand specify a precision value of
4.In this example, we’ll select Fractionas our
format.)
MODES
Select
Fraction
4
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2. Enter the calculation.
3
2
3
4
8
5
7
Note: Ensure you are in
the HOME view.
3. Evaluate the calculation.
Note that if you had
selected Mixed
Fractioninstead of
Fractionas the
Number format, the answer would have been
expressed as 25+7/8.
Converting
decimals to
fractions
To convert a decimal value to a fraction:
1. Set the number format mode to Fraction or Mixed
Fraction.
2. Either retrieve the value from the History, or enter the
value on the command line.
3. Press
to convert the number to a fraction.
When converting a decimal to a fraction, keep the
following points in mind:
•
When converting a recurring decimal to a fraction,
set the fraction precision to about 6, and ensure that
you include more than six decimal places in the
recurring decimal that you enter.
In this example, the
fraction precision is set
to 6. The top
calculation returns the
correct result. The
bottom one does not.
•
To convert an exact decimal to a fraction, set the
fraction precision to at least two more than the
number of decimal places in the decimal.
1-28
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In this example, the
fraction precision is set
to 6.
Complex numbers
Complex results
The HP 39gs can return a complex number as a result for
some math functions. A complex number appears as an
ordered pair (x, y), where x is the real part and y is the
imaginary part. For example, entering –1 returns (0,1).
To enter complex
numbers
Enter the number in either of these forms, where x is the
real part, y is the imaginary part, and i is the imaginary
constant, –1 :
•
•
(x, y) or
x + iy.
To enter i:
•
•
press
or
press
,
or
keys to select Constant,
to
to move to the right column of the menu,
select i, and
.
Storing complex
numbers
There are 10 variables available for storing complex
numbers: Z0 to Z9. To store a complex number in a
variable:
•
Enter the complex number, press
, enter the
variable to store the number in, and press
.
4
5
Z 0
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Catalogs and editors
The HP 39gs has several catalogs and editors. You use
them to create and manipulate objects. They access
features and stored values (numbers or text or other items)
that are independent of aplets.
•
A catalog lists items, which you can delete or
transmit, for example an aplet.
•
An editor lets you create or modify items and
numbers, for example a note or a matrix.
Catalog/Editor
Contents
Aplet library
Aplets.
(
)
Sketch editor
Sketches and diagrams, See
Chapter 17, “Notes and
sketches”.
(
SKETCH)
Lists. In HOME, lists are
enclosed in {}. See Chapter 16,
“Lists”.
List (
LIST)
One- and two-dimensional
arrays. In HOME, arrays are
enclosed in []. See Chapter 15,
“Matrices”.
Matrix (
MATRIX)
Notes (short text entries). See
Chapter 17, “Notes and
sketches”.
Notepad (
NOTEPAD)
Programs that you create, or
associated with user-defined
aplets. See Chapter 18,
“Programming”.
Program (
PROGRM)
1-30
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2
Aplets and their views
Aplet views
This section examines the options and functionality of the
three main views for the Function, Polar, Parametric, and
Sequence aplets: Symbolic, Plot, and Numeric views.
About the Symbolic view
The Symbolic view is the defining view for the Function,
Parametric, Polar, and Sequence aplets. The other views
are derived from the symbolic expression.
You can create up to 10 different definitions for each
Function, Parametric, Polar, and Sequence aplet. You
can graph any of the relations (in the same aplet)
simultaneously by selecting them.
Defining an expression (Symbolic view)
Choose the aplet from the Aplet Library.
Press
or
to
select an aplet.
The Function,
Parametric, Polar, and Sequence aplets start in the
Symbolic view.
If the highlight is on an existing expression, scroll to
an empty line—unless you don’t mind writing over the
expression—or, clear one line (
) or all lines
(
CLEAR).
Expressions are selected (check marked) on entry. To
deselect an expression, press
expressions are plotted.
. Allselected
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2-1
– For a Function
definition, enter
an expression to
define F(X). The
only independent
variable in the
expression is X.
– For a
Parametric
definition, enter
a pair of
expressions to
define X(T) and
Y(T). The only
independent variable in the expressions is T.
– For a Polar
definition, enter
an expression to
define R(θ). The
only independent
variable in the
expression is θ.
– For a Sequence
definition, either
enter the first term,
or the first and
second terms, for U
(U1, or...U9, or
U0). Then define
the nth term of the sequence in terms of N or of
the prior terms, U(N–1) and/or U(N–2). The
expressions should produce real-valued
sequences with integer domains. Or define the
nth term as a non-recursive expression in terms of
n only. In this case, the calculator inserts the first
two terms based on the expression that you
define.
–
Note: You will have to enter the second term if
the hp39gs is unable to calculate it automatically.
Typically if Ux(N) depends on Ux(N–2) then you
must enter Ux(2).
2-2
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Evaluating expressions
In aplets
In the Symbolic view, a variable is a symbol only, and
does not represent one specific value. To evaluate a
function in Symbolic view, press . If a function calls
another function, then resolves all references to
other functions in terms of their independent variable.
1. Choose the Function
aplet.
Select Function
2. Enter the expressions in the Function aplet’s Symbolic
view.
A
B
F1
F2
3. Highlight F3(X).
4. Press
Note how the values
for F1(X) and F2(X) are
substituted into F3(X).
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In HOME
You can also evaluate any expression in HOME by
entering it into the edit line and pressing
.
For example, define F4 as below. In HOME, type
F4(9)and press . This evaluates the expression,
substituting 9in place of Xinto F4.
SYMB view keys The following table details the menu keys that you use to
work with the Symbolic view.
Key
Meaning
Copies the highlighted expression to
the edit line for editing. Press
when done.
Checks/unchecks the current
expression (or set of expressions).
Only checked expression(s) are
evaluated in the Plot and Numeric
views.
Enters the independent variable in the
Function aplet. Or, you can use the
key on the keyboard.
Enters the independent variable in the
Parametric aplet. Or, you can use the
key on the keyboard.
Enters the independent variable in the
Polar aplet. Or, you can use the
key on the keyboard.
Enters the independent variable in the
Sequence aplet. Or, you can use the
key on the keyboard.
Displays the current expression in text
book form.
Resolves all references to other
definitions in terms of variables and
evaluates all arithmetic expressions.
Displays a menu for entering variable
names or contents of variables.
2-4
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Key
Meaning (Continued)
Displays the menu for entering math
operations.
CHARS
Displays special characters. To enter
one, place the cursor on it and press
. To remain in the CHARS menu
and enter another special character,
press
.
Deletes the highlighted expression or
the current character in the edit line.
CLEAR
Deletes all expressions in the list or
clears the edit line.
About the Plot view
After entering and selecting (check marking) the
expression in the Symbolic view, press
. To adjust
the appearance of the graph or the interval that is
displayed, you can change the Plot view settings.
You can plot up to ten expressions at the same time.
Select the expressions you want to be plotted together.
Setting up the plot (Plot view setup)
Press
SETUP-PLOT to define any of the settings
shown in the next two tables.
1. Highlight the field to edit.
–
–
If there is a number to enter, type it in and press
or
.
If there is an option to choose, press
highlight your choice, and press
,
or
.
As a shortcut to
change and press
options.
, just highlight the field to
to cycle through the
–
If there is an option to select or deselect, press
to check or uncheck it.
2. Press
to view more settings.
to view the new plot.
3. When done, press
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2-5
Plot view
settings
The plot view settings are:
Field
Meaning
XRNG, YRNG
Specifies the minimum and
maximum horizontal (X) and
vertical (Y) values for the plotting
window.
RES
For function plots: Resolution;
“Faster” plots in alternate pixel
columns; “Detail” plots in every
pixel column.
TRNG
θRNG
Parametric aplet: Specifies the t-
values (T) for the graph.
Polar aplet: Specifies the angle (θ)
value range for the graph.
NRNG
TSTEP
θSTEP
Sequence aplet: Specifies the
index (N) values for the graph.
For Parametric plots: the increment
for the independent variable.
For Polar plots: the increment
value for the independent
variable.
SEQPLOT
For Sequence aplet: Stairstep or
Cobweb types.
XTICK
YTICK
Horizontal spacing for tickmarks.
Vertical spacing for tickmarks.
Those items with space for a checkmark are settings you
can turn on or off. Press
page.
to display the second
Field
Meaning
SIMULT
If more than one relation is being
plotted, plots them simultaneously
(otherwise sequentially).
INV. CROSS
Cursor crosshairs invert the status
of the pixels they cover.
2-6
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Field
Meaning (Continued)
CONNECT
Connect the plotted points. (The
Sequence aplet always connects
them.)
LABELS
Label the axes with XRNGand
YRNGvalues.
AXES
GRID
Draw the axes.
Draw grid points using XTICK
and YTICKspacing.
Reset plot
settings
To reset the default values for all plot settings, press
CLEAR in the Plot Setup view. To reset the default
value for a field, highlight the field, and press
.
Exploring the graph
Plot view gives you a selection of keys and menu keys to
explore a graph further. The options vary from aplet to
aplet.
PLOT view keys
The following table details the keys that you use to work
with the graph.
Key
Meaning
CLEAR
Erases the plot and axes.
Offers additional pre-defined views
for splitting the screen and for scaling
(“zooming”) the axes.
Moves cursor to far left or far right.
Moves cursor between relations.
Interrupts plotting.
or
Continues plotting if interrupted.
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Key
Meaning (Continued)
Turns menu-key labels on and off.
When the labels are off, pressing
turns them back on.
•
Pressing
once displays the
full row of labels.
•
Pressing
a second time
removes the row of labels to
display only the graph.
•
Pressing
a third time
displays the coordinate mode.
appears over the
on
.
Opens an input form for you to enter
an X (or T or N or θ) value. Enter the
value and press
. The cursor jumps
to the point on the graph that you
entered.
Function aplet only: turns on menu list
for root-finding functions (see
“Analyse graph with FCN functions”
on page 3-4).
Displays the current, defining
expression. Press
menu.
to restore the
Trace a graph
You can trace along a function using the
or
key
which moves the cursor along the graph. The display also
shows the current coordinate position (x, y) of the cursor.
Trace mode and the coordinate display are automatically
set when a plot is drawn.
Note: Tracing might not appear to exactly follow your
plot if the resolution (in Plot Setup view) is set to Faster.
This is because RES: FASTER plots in only every other
column, whereas tracing always uses every column.
In Function and Sequence Aplets: You can also
scroll (move the cursor) left or right beyond the edge of
the display window in trace mode, giving you a view of
more of the plot.
To move between
relations
If there is more than one relation displayed, press
to move between relations.
or
2-8
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To jump directly to
a value
To jump straight to a value rather than using the Trace
function, use the
a value. Press
menu key. Press
, then enter
to jump to the value.
To turn trace on/off
If the menu labels are not displayed, press
first.
•
•
•
Turn off trace mode by pressing
Turn on trace mode by pressing
.
.
To turn the coordinate display off, press
.
Zoom within a
graph
One of the menu key options is
the plot on a larger or smaller scale. It is a shortcut for
changing the Plot Setup.
. Zooming redraws
The Set Factors...option enables you to set the
factors by which you zoom in or zoom out, and whether
the zoom is centered about the cursor.
ZOOM options
Press
, select an option, and press
. (If
is not displayed, press
available in all aplets.
.) Not all
Option
Meaning
Center
Re-centers the plot around the
current position of the cursor without
changing the scale.
Box...
In
Lets you draw a box to zoom in on.
See “Other views for scaling and
splitting the graph” on page 2-13.
Divides horizontal and vertical
scales by the X-factor and Y-factor.
For instance, if zoom factors are 4,
then zooming in results in 1/4 as
many units depicted per pixel. (see
Set Factors...)
Out
Multiplies horizontal and vertical
scales by the X-factor and Y-factor
(see Set Factors...).
X-Zoom In
Divides horizontal scale only, using
X-factor.
X-Zoom Out
Multiplies horizontal scale, using
X-factor.
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Option
Meaning (Continued)
Y-Zoom In
Divides vertical scale only, using
Y-factor.
Y-Zoom Out
Square
Multiplies vertical scale only, using
Y-factor.
Changes the vertical scale to match
the horizontal scale. (Use this after
doing a Box Zoom, X-Zoom, or
Y-Zoom.)
Set
Factors...
Sets the X-Zoom and Y-Zoom factors
for zooming in or zooming out.
Includes option to recenter the plot
before zooming.
Auto Scale
Rescales the vertical axis so that the
display shows a representative
piece of the plot, for the supplied x
axis settings. (For Sequence and
Statistics aplets, autoscaling
rescales both axes.)
The autoscale process uses the first
selected function only to determine
the best scale to use.
Decimal
Rescales both axes so each pixel =
0.1 units. Resets default values for
XRNG
(–6.5 to 6.5) and YRNG (–3.1 to
3.2). (Not in Sequence or Statistics
aplets.)
Integer
Trig
Rescales horizontal axis only,
making each pixel =1 unit. (Not
available in Sequence or Statistics
aplets.)
Rescales horizontal axis so
1 pixel = π/24 radians, 7.58, or
1
8 / grads; rescales vertical axis
3
so
1 pixel = 0.1 unit.
(Not in Sequence or Statistics
aplets.)
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Option
Meaning (Continued)
Un-zoom
Returns the display to the previous
zoom, or if there has been only one
zoom, un-zoom displays the graph
with the original plot settings.
ZOOM examples
The following screens show the effects of zooming options
on a plot of 3sinx .
Plot of 3sinx
Zoom In:
In
Un-zoom:
Un-zoom
Note: Press
to move to
the bottom of the Zoom list.
Zoom Out:
Out
Now un-zoom.
X-Zoom In:
X-Zoom In
Now un-zoom.
X-Zoom Out:
X-Zoom Out
Now un-zoom.
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Y-Zoom In:
Y-Zoom In
Now un-zoom.
Y-Zoom Out:
Y-Zoom Out
Zoom Square:
Square
To box zoom
The Box Zoom option lets you draw a box around the
area you want to zoom in on by selecting the endpoints
of one diagonal of the zoom rectangle.
1. If necessary, press
labels.
to turn on the menu-key
2. Press
3. Position the cursor on one corner of the rectangle.
Press
4. Use the cursor keys
, etc.) to drag to
the opposite corner.
and select Box...
.
(
5. Press
to zoom in
on the boxed area.
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To set zoom factors
1. In the Plot view, press
2. Press
3. Select Set Factors...and press
.
.
.
4. Enter the zoom factors. There is one zoom factor for
the horizontal scale (XZOOM) and one for the vertical
scale (YZOOM).
Zooming out multiplies the scale by the factor, so that
a greater scale distance appears on the screen.
Zooming in divides the scale by the factor, so that a
shorter scale distance appears on the screen.
Other views for scaling and splitting the graph
The preset viewing options menu (
) contains
options for drawing the plot using certain pre-defined
configurations. This is a shortcut for changing Plot view
settings. For instance, if you have defined a trigonometric
function, then you could select Trigto plot your function
on a trigonometric scale. It also contains split-screen
options.
In certain aplets, for example those that you download
from the world wide web, the preset viewing options
menu can also contain options that relate to the aplet.
VIEWS menu
options
Press
, select an option, and press
.
Option
Meaning
Plot-
Detail
Splits the screen into the plot and a
close-up.
Plot-Table
Splits the screen into the plot and
the data table.
Overlay
Plot
Plots the current expression(s)
without erasing any pre-existing
plot(s).
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Option
Meaning (Continued)
Auto Scale
Rescales the vertical axis so that the
display shows a representative
piece of the plot, for the supplied x
axis settings. (For Sequence and
Statistics aplets, autoscaling
rescales both axes.)
The autoscale process uses the first
selected function only to determine
the best scale to use.
Decimal
Rescales both axes so each pixel =
0.1 unit. Resets default values for
XRNG
(–6.5 to 6.5) and YRNG (–3.1 to
3.2). (Not in Sequence or Statistics
aplets.)
Integer
Trig
Rescales horizontal axis only,
making each pixel=1 unit. (Not
available in Sequence or Statistics
aplets.)
Rescales horizontal axis so
1 pixel=π/24 radian, 7.58, or
1
8 / grads; rescales vertical axis so
3
1 pixel =0.1 unit.
(Not in Sequence or Statistics
aplets.)
Split the screen
The Plot-Detail view can give you two simultaneous views
of the plot.
1. Press
. Select Plot-Detailand press
.
The graph is plotted twice. You can now zoom in on
the right side.
2. Press
,
select the zoom method
and press
or
. This zooms the
right side. Here is an
example of split screen with Zoom In.
–
The Plot menu keys are available as for the full
plot (for tracing, coordinate display, equation
display, and so on).
2-14
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–
–
moves the leftmost cursor to the
screen’s left edge and
moves the
rightmost cursor to the screen’s right edge.
The
plot.
menu key copies the right plot to the left
3. To un-split the screen, press
over the whole screen.
. The left side takes
The Plot-Table view gives you two simultaneous views of
the plot.
1. Press
. Select
Plot-Tableand
press
. The screen
displays the plot on the
left side and a table of
numbers on the right side.
2. To move up and down the table, use the
and
cursor keys. These keys move the tra.ce point left or
right along the plot, and in the table, the
corresponding values are highlighted.
3. To move between functions, use the
and
cursor keys to move the cursor from one graph to
another.
4. To return to a full Numeric (or Plot) view, press
(or
).
Overlay plots
If you want to plot over an existing plot without erasing
that plot, then use Overlay Plotinstead of
. Note that tracing follows only the current
functions from the current aplet.
Decimal scaling
Integer scaling
Decimal scaling is the default scaling. If you have
changed the scaling to Trig or Integer, you can change it
back with Decimal.
Integer scaling compresses the axes so that each pixel is
1× 1 and the origin is near the screen center.
Trigonometric
scaling
Use trigonometric scaling whenever you are plotting an
expression that includes trigonometric functions.
Trigonometric plots are more likely to intersect the axis at
points factored by π.
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About the numeric view
Afterenteringandselecting
(check marking) the
expression or expressions
that you want to explore in
the Symbolic view, press
to view a table of
data values for the independent variable (X, T, θ, or N)
and dependent variables.
Setting up the table (Numeric view setup)
Press
NUM to define
any of the table settings.
Use the Numeric Setup
input form to configure the
table.
1. Highlight the field to edit. Use the arrow keys to
move from field to field.
–
If there is a number to enter, type it in and press
or . To modify an existing number,
press
.
–
If there is an option to choose, press
highlight your choice, and press
,
or
.
– Shortcut: Press the
key to copy values
from the Plot Setup into NUMSTARTand
NUMSTEP. Effectively, the
allows you to make the table match the pixel
columns in the graph view.
menu key
2. When done, press
numbers.
to view the table of
2-16
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Numeric view
settings
The following table details the fields on the Numeric
Setup input form.
Field
Meaning
NUMSTART
The independent variable’s
starting value.
NUMSTEP
NUMTYPE
The size of the increment from
one independent variable value
to the next.
Type of numeric table: Automatic
or Build Your Own. To build your
own table, you must type each
independent value into the table
yourself.
NUMZOOM
Allows you to zoom in or out on a
selected value of the independent
variable.
Reset numeric
settings
To reset the default values for all table settings, press
CLEAR.
Exploring the table of numbers
NUM view
menu keys
The following table details the menu keys that you use to
work with the table of numbers.
Key
Meaning
Displays ZOOM menu list.
Toggles between two character
sizes.
Displays the defining function
expression for the highlighted
column. To cancel this display, press
.
Zoom within a
table
Zooming redraws the table of numbers in greater or
lesser detail.
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ZOOM options
The following table lists the zoom options:
Option
Meaning
In
Decreases the intervals for the
independent variable so a narrower
range is shown. Uses the NUMZOOM
factor in Numeric Setup.
Out
Increases the intervals for the
independent variable so that a
wider range is shown. Uses the
NUMZOOMfactor in Numeric Setup.
Decimal
Integer
Trig
Changes intervals for the
independent variable to 0.1 units.
Starts at zero. (Shortcut to changing
NUMSTARTand NUMSTEP.)
Changes intervals for the
independent variable to 1 unit.
Starts at zero. (Shortcut to changing
NUMSTEP.)
Changes intervals for independent
variable to π/24 radian or 7.5
1
degrees or 8 / grads. Starts at
3
zero.
Un-zoom
Returns the display to the previous
zoom.
The display on the right is a Zoom In of the display on the
left. The ZOOMfactor is 4.
H I N T
To jump to an independent variable value in the table,
use the arrow keys to place the cursor in the independent
variable column, then enter the value to jump to.
Automatic
recalculation
You can enter any new value in the X column. When you
press
, the values for the dependent variables are
recalculated, and the entire table is regenerated with the
same interval between X values.
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Building your own table of numbers
The default NUMTYPEis “Automatic”, which fills the table
with data for regular intervals of the independent (X, T, θ,
or N) variable. With the NUMTYPEoption set to “Build
Your Own”, you fill the table yourself by typing in the
independent-variable values you want. The dependent
values are then calculated and displayed.
Build a table
1. Start with an expression defined (in Symbolic view) in
the aplet of your choice. Note: Function, Polar,
Parametric, and Sequence aplets only.
2. In the Numeric Setup (
NUM), choose
NUMTYPE: Build Your Own.
3. Open the Numeric view (
).
4. Clear existing data in the table (
CLEAR).
5. Enter the independent values in the left-hand column.
Type in a number and press
to enter them in order, because the
can rearrange them. To insert a number between two
. You do not have
function
others, use
.
F1 and F2
entries are
generated
automatically
You enter
numbers into
the X column
Clear data
Press
CLEAR,
to erase the data from a table.
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“Build Your Own” menu keys
Key
Meaning
Puts the highlighted independent
value (X, T, θ, or N) into the edit
line. Pressing
replaces
this variable with its current value.
Inserts a zero value at the position
of the highlight. Replace a zero
by typing the number you want
and pressing
.
Sorts the independent variable
values into ascending or
descending order. Press
and select the ascending or
descending option from the
menu, and press
.
Toggles between two character
sizes.
Displays the defining function
expression for the highlighted
column.
Deletes the highlighted row.
Clears all data from the table.
CLEAR
Example: plotting a circle
2
2
Plot the circle, x + y = 9. First rearrange it to read
y = ± 9 – x2 .
To plot both the positive and negative y values, you need
to define two equations as follows:
y = 9 – x2 and y = – 9 – x2
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1. In the Function aplet, specify the functions.
Select
Function
9
9
2. Reset the graph setup to the default settings.
SETUP-PLOT
CLEAR
3. Plot the two functions
and hide the menu so
that you can see all the
circle.
4. Reset the numeric setup to the default settings.
SETUP-NUM
CLEAR
5. Display the functions in numeric form.
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3
Function aplet
About the Function aplet
The Function aplet enables you to explore up to 10
example y = 2x + 3 .
Once you have defined a function you can:
•
create graphs to find roots, intercepts, slope, signed
area, and extrema
•
create tables to evaluate functions at particular
values.
This chapter demonstrates the basic tools of the Function
aplet by stepping you through an example. See “Aplet
views” on page 2-1 for further information about the
functionality of the Symbolic, Numeric, and Plot views.
Getting started with the Function aplet
The following example involves two functions: a linear
function y = 1 – x and a quadratic equation
y = (x + 3)2 – 2 .
Open the
Function aplet
1. Open the Function aplet.
Select Function
The Function aplet starts
in the Symbolic view.
The Symbolic view is the defining view for Function,
Parametric, Polar, and Sequence aplets. The other
views are derived from the symbolic expression.
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Define the
expressions
2. There are 10 function definition fields on the Function
aplet’s Symbolic view screen. They are labeled F1(X)
to F0(X). Highlight the function definition field you
want to use, and enter an expression. (You can press
to delete an existing line, or
clear all lines.)
CLEAR to
1
3
2
Set up the plot
You can change the scales of the x and y axes, graph
resolution, and the spacing of the axis ticks.
3. Display plot settings.
SETUP-PLOT
Note: For our example, you can leave the plot
settings at their default values since we will be using
the Auto Scale feature to choose an appropriate y
axis for our x axis settings. If your settings do not
match this example, press
default values.
CLEAR to restore the
4. Specify a grid for the graph.
Plot the
functions
5. Plot the functions.
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Change the
scale
6. You can change the scale to see more or less of your
graphs. In this example, choose Auto Scale. (See
“VIEWS menu options” on page 2-13 for a
description of Auto Scale).
Select Auto
Scale
Trace a graph
7. Trace the linear function.
6 times
Note: By default, the
tracer is active.
8. Jump from the linear function to the quadratic
function.
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Analyse graph
with FCN
functions
9. Display the Plot view menu.
From the Plot view menu, you can use the functions
on the FCN menu to find roots, intersections, slopes,
and areas for a function defined in the Function aplet
(and any Function-based aplets). The FCN functions
act on the currently selected graph. See “FCN
functions” on page 3-10 for further information.
To find a root of the
quadratic function
10.Move the cursor to the graph of the quadratic
equation by pressing the
the cursor so that it is near x = –1 by pressing the
or key.
or
key. Then move
SelectRoot
The root value is
displayed at the
bottom of the screen.
Note: If there is more
than one root (as in our
example), the
coordinates of the root closest to the current cursor
position are displayed.
To find the
11.Find the intersection of the two functions.
intersection of the
two functions
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12.Choose the linear function whose intersection with the
quadratic function you wish to find.
The coordinates of the
intersection point are
displayed at the
bottom of the screen.
Note: If there is more
than one intersection
(as in our example), the coordinates of the
intersection point closest to the current cursor position
are displayed.
To find the slope of
the quadratic
function
13.Find the slope of the quadratic function at the
intersection point.
Select Slope
The slope value is
displayed at the
bottom of the screen.
To find the signed
area of the two
functions
14.To find the area between the two functions in the
range –2 ≤ x ≤ –1, first move the cursor to
F1(x) = 1 – x and select the signed area option.
Select Signedarea
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15.Move the cursor to x = –2 by pressing the
key.
or
2
16.Press
to accept using F2(x) = (x + 3) – 2 as the
other boundary for the integral.
17. Choose the end value
for x.
1
The cursor jumps to
x = –1 on the linear
function.
18.Display the numerical
value of the integral.
Note: See “Shading
area” on page 3-11
for another method of
calculating area.
To find the
extremum of the
quadratic
19.Move the cursor to the quadratic equation and find
the extremum of the quadratic.
Select Extremum
The coordinates of the
extremum are
displayed at the
bottom of the screen.
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H I N T
The Root and Extremum functions return one value only
even if the function has more than one root or extremum.
The function finds the value closest to the position of the
cursor. You need to re-locate the cursor to find other roots
or extrema that may exist.
Display the
numeric view
20.Display the numeric view.
Set up the table
21.Display the numeric setup.
SETUP-NUM
See “Setting up the table (Numeric view setup)” on
page 2-16 for more information.
22.Match the table settings to the pixel columns in the
graph view.
Explore the
table
23.Display the table of values.
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To navigate around
a table
24.Move to X = –5.9.
6 times
To go directly to a
value
25.Move directly to X = 10.
1 0
To access the zoom
options
26.Zoom in on X = 10 by a factor of 4. Note: NUMZOOM
has a setting of 4.
In
To change font size
27. Display table numbers in large font.
To display the
symbolic definition
of a column
28.Display the symbolic definition for the F1 column.
The symbolic definition of
F1 is displayed at the
bottom of the screen.
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Function aplet interactive analysis
From the Plot view (
), you can use the functions on
the FCN menu to find roots, intersections, slopes, and
areas for a function defined in the Function aplet (and any
Function-based aplets). See “FCN functions” on page 3-
10. The FCN operations act on the currently selected
graph.
The results of the FCN functions are saved in the following
variables:
•
•
•
•
•
Area
Extremum
Isect
Root
Slope
For example, if you use the Root function to find the root
of a plot, you can use the result in calculations in HOME.
Access FCN
variables
The FCN variables are contained on the VARS menu.
To access FCN variables in HOME:
Select Plot FCN
or
to choose a
variable
To access FCN variable in the Function aplet’s Symbolic
view:
Select Plot FCN
or
to choose a variable
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FCN functions
The FCN functions are:
Function
Description
Root
Select Rootto find the root of the
current function nearest the
cursor. If no root is found, but only
an extremum, then the result is
labeled EXTR:instead of ROOT:.
(The root-finder is also used in the
Solve aplet. See also “Interpreting
results” on page 7-6.) The cursor
is moved to the root value on the
x-axis and the resulting x-value is
saved in a variable named
ROOT.
Extremum
Select Extremumto find the
maximum or minimum of the
current function nearest the
cursor. This displays the
coordinate values and moves the
cursor to the extremum. The
resulting value is saved in a
variable named EXTREMUM.
Slope
Select Slopeto find the numeric
derivative at the current position
of the cursor. The result is saved in
a variable named SLOPE.
Signed area
Select Signed areato find the
numeric integral. (If there are two
or more expressions
checkmarked, then you will be
asked to choose the second
expression from a list that
includes the x-axis.) Select a
starting point, then move the
cursor to selection ending point.
The result is saved in a variable
named AREA.
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Function
Description (Continued)
Intersection
Select Intersectionto find the
intersection of two graphs nearest
the cursor. (You need to have at
least two selected expressions in
Symbolic view.) Displays the
coordinate values and moves the
cursor to the intersection. (Uses
Solve function.) The resulting x-
value is saved in a variable
named ISECT.
Shading area
You can shade a selected area between functions. This
process also gives you an approximate measurement of
the area shaded.
1. Open the Function aplet. The Function aplet opens in
the Symbolic view.
2. Select the expressions whose curves you want to
study.
3. Press
4. Press
to plot the functions.
or
to position the cursor at the starting
point of the area you want to shade.
5. Press
.
6. Press
.
, then select Signed areaand press
7. Press
, choose the function that will act as the
boundary of the shaded area, and press
.
8. Press the
9. Press
or
key to shade in the area.
to calculate the area. The area
measurement is displayed near the bottom of the
screen.
To remove the shading, press
to re-draw the plot.
Function aplet
3-11
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Plotting a piecewise-defined function
Suppose you wanted to plot the following piecewise-
defined function.
⎧
⎪
⎨
⎪
⎩
x + 2 ;x ≤ –1
x2
;–1 < x ≤ 1
f(x) =
4 – x ;x ≥ 1
1. Open the Function
aplet.
Select
Function
2. Highlight the line you want to use, and enter the
expression. (You can press
to delete an existing
line, or CLEAR to clear all lines.)
2
1
CHARS ≤
CHARS >
1
AND
CHARS ≤ 1
4
CHARS > 1
Note: You can use the
menu key to assist in the
entry of equations. It has the same effect as pressing
.
3-12
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4
Parametric aplet
About the Parametric aplet
The Parametric aplet allows you to explore parametric
equations. These are equations in which both x and y are
defined as functions of t. They take the forms x = f(t)
and y = g(t) .
Getting started with the Parametric aplet
The following example uses the parametric equations
x(t) = 3sint
y(t) = 3cost
Note: This example will produce a circle. For this
example to work, the angle measure must be set to
degrees.
Open the
Parametric aplet
1. Open the Parametric aplet.
Select
Parametric
Define the
expressions
2. Define the expressions.
3
3
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Set angle
measure
3. Set the angle measure to degrees.
MODES
Select Degrees
Set up the plot
4. Display the graphing options.
PLOT
The Plot Setup input form has two fields not included
in the Function aplet, TRNGand TSTEP. TRNG
specifies the range of t values. TSTEPspecifies the
step value between t values.
5. Set the TRNGand TSTEPso that t steps from 0° to
360° in 5° steps.
360
5
Plot the
expression
6. Plot the expression.
7. To see all the circle, press
twice.
4-2
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Overlay plot
8. Plot a triangle graph over the existing circle graph.
PLOT
120
Select OverlayPlot
A triangle is displayed
rather than a circle (without changing the equation)
because the changed value of TSTEPensures that
points being plotted are 120° apart instead of nearly
continuous.
You are able to explore the graph using trace, zoom,
split screen, and scaling functionality available in the
Function aplet. See “Exploring the graph” on page 2-
7 for further information.
Display the
numbers
9. Display the table of values.
You can highlight a
t-value, type in a
replacement value,
and see the table jump
to that value. You can also zoom in or zoom out on
any t-value in the table.
You are able to explore the table using
, build your own table, and split screen
,
functionality available in the Function aplet. See
“Exploring the table of numbers” on page 2-17 for
further information.
Parametric aplet
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5
Polar aplet
Getting started with the Polar aplet
Open the Polar
aplet
1. Open the Polar aplet.
Select Polar
Like the Function aplet,
the Polar aplet opens
in the Symbolic view.
Define the
expression
2. Define the polar equation r = 2πcos(θ ⁄ 2)cos(θ)2 .
2
π
2
Specify plot
settings
3. Specify the plot settings. In this example, we will use
the default settings, except for the θRNGfields.
SETUP-PLOT
CLEAR
4
π
Plot the
expression
4. Plot the expression.
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Explore the
graph
5. Display the Plot view menu key labels.
The Plot view options
available are the same
as those found in the
Function aplet. See
“Exploring the graph”
on page 2-7 for further information.
Display the
numbers
6. Display the table of values for θ and R1.
The Numeric view
options available are
the same as those
found in the Function
aplet. See “Exploring the table of numbers” on
page 2-17 for further information.
5-2
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6
Sequence aplet
About the Sequence aplet
The Sequence aplet allows you to explore sequences.
You can define a sequence named, for example, U1:
•
•
•
•
•
in terms of n
in terms of U1(n–1)
in terms of U1(n–2)
in terms of another sequence, for example, U2(n)
in any combination of the above.
The Sequence aplet allows you to create two types of
graphs:
–
A Stairsteps graph plots n on the horizontal
axis and U on the vertical axis.
n
–
A Cobweb graph plots U
on the horizontal
n–1
axis and U on the vertical axis.
n
Getting started with the Sequence aplet
The following example defines and then plots an
expression in the Sequence aplet. The sequence
illustrated is the well-known Fibonacci sequence where
each term, from the third term on, is the sum of the
preceding two terms. In this example, we specify three
sequence fields: the first term, the second term and a rule
for generating all subsequent terms.
However, you can also define a sequence by specifying
just the first term and the rule for generating all
subsequent terms. You will, though, have to enter the
second term if the hp39gs is unable to calculate it
automatically. Typically if the nth term in the sequence
depends on n–2, then you must enter the second term.
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6-1
Open the
Sequence aplet
1. Open the Sequence aplet.
Select
Sequence
The Sequence aplet
starts in the Symbolic
view.
Define the
expression
2. Define the Fibonacci sequence, in which each term
(after the first two) is the sum of the preceding two
terms:
U1 = 1, U2 = 1, Un = Un – 1 + Un – 2 for n > 3 .
In the Symbolic view of the Sequence aplet, highlight
the U1(1) field and begin defining your sequence.
1
1
Note: You can use the
,
,
,
, and
equations.
menu keys to assist in the entry of
Specify plot
settings
3. In Plot Setup, first set the SEQPLOToption to
Stairstep. Reset the default plot settings by
clearing the Plot Setup view.
SETUP-PLOT
CLEAR
8
8
6-2
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Plot the
sequence
4. Plot the Fibonacci
sequence.
5. In Plot Setup, set the SEQPLOT option to Cobweb.
SETUP-PLOT
Select Cobweb
Display the table 6. Display the table of values for this example.
Sequence aplet
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7
Solve aplet
About the Solve aplet
The Solve aplet solves an equation or an expression for
its unknown variable. You define an equation or
expression in the symbolic view, then supply values for all
the variables except one in the numeric view. Solve works
only with real numbers.
Note the differences between an equation and an
expression:
•
An equation contains an equals sign. Its solution is a
value for the unknown variable that makes both sides
have the same value.
•
An expression does not contain an equals sign. Its
solution is a root, a value for the unknown variable
that makes the expression have a value of zero.
You can use the Solve aplet to solve an equation for any
one of its variables.
When the Solve aplet is started, it opens in the Solve
Symbolic view.
•
In Symbolic view, you specify the expression or
equation to solve. You can define up to ten equations
(or expressions), named E0 to E9. Each equation can
contain up to 27 real variables, named A to Z and θ.
•
In Numeric view, you specify the values of the known
variables, highlight the variable that you want to
solve for, and press
.
You can solve the equation as many times as you want,
using new values for the knowns and highlighting a
different unknown.
Note: It is not possible to solve for more than one variable
at once. Simultaneous linear equations, for example,
should be solved using the Linear Solver aplet, matrices
or graphs in the Function aplet.
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7-1
Getting started with the Solve aplet
Suppose you want to find the acceleration needed to
increase the speed of a car from 16.67 m/sec (60 kph)
to 27.78 m/sec (100 kph) in a distance of 100 m.
The equation to solve is:
V2 = U2 + 2AD
Open the Solve
aplet
1. Open the Solve aplet.
Select Solve
The Solve aplet starts in
the symbolic view.
Define the
equation
2. Define the equation.
V
U
2
A
D
Note: You can use the
entry of equations.
menu key to assist in the
Enter known
variables
3. Display the Solve numeric view screen.
7-2
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4. Enter the values for the known variables.
2 7
1 6
7 8
6 7
1 0 0
H I N T
If the Decimal Mark setting in the Modes input form
MODES) is set to Comma, use instead of
(
.
Solve the
unknown
variable
5. Solve for the unknown variable (A).
Therefore, the acceleration needed to increase the
speed of a car from 16.67 m/sec (60 kph) to 27.78
m/sec
(100 kph) in a distance of 100 m is approximately
2
2.47 m/s .
Because the variable A in the equation is linear we
know that we need not look for any other solutions.
Plot the
equation
The Plot view shows one graph for each side of the
selected equation. You can choose any of the
variables to be the independent variable.
The current equation is V2 = U2 + 2AD .
One of these is Y = V2 , with V = 27.78 , that is,
Y = 771.7284 . This graph will be a horizontal line.
The other graph will be Y = U2 + 2AD , with
U = 16.67 and D = 100, that is,
Y = 200A + 277.8889 . This graph is also a line. The
desired solution is the value of A where these two
lines intersect.
Solve aplet
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6. Plot the equation for variable A.
Select Auto
Scale
7. Trace along the graph
representing the left
side of the equation
until the cursor nears
the intersection.
20 times
Note the value of A displayed near the bottom left
corner of the screen.
The Plot view provides a convenient way to find an
approximation to a solution instead of using the
Numeric view Solve option. See “Plotting to find
guesses” on page 7-7 for more information.
Solve aplet’s NUM view keys
The Solve aplet’s NUM view keys are:
Key
Meaning
Copies the highlighted value to the
edit line for editing. Press
done.
when
Displays a message about the
solution (see “Interpreting results” on
page 7-6).
Displays other pages of variables, if
any.
Displays the symbolic definition of the
current expression. Press
done.
when
Finds a solution for the highlighted
variable, based on the values of the
other variables.
7-4
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Key
Meaning (Continued)
Clears highlighted variable to zero or
deletes current character in edit line,
if edit line is active.
CLEAR
Resets all variable values to zero or
clears the edit line, if cursor is in edit
line.
Use an initial guess
You can usually obtain a faster and more accurate
solution if you supply an estimated value for the unknown
variable before pressing
a solution at the initial guess.
. Solve starts looking for
Before plotting, make sure the unknown variable is
highlighted in the numeric view. Plot the equation to help
you select an initial guess when you don’t know the range
in which to look for the solution. See “Plotting to find
H I N T
An initial guess is especially important in the case of a
curve that could have more than one solution. In this case,
only the solution closest to the initial guess is returned.
Number format
You can change the number format for the Solve aplet in
the Numeric Setup view. The options are the same as in
HOME MODES: Standard, Fixed, Scientific, and
Engineering. For the latter three, you also specify how
many digits of accuracy you want. See “Mode settings”
on page 1-10 for more information.
You might find it handy to set a different number format
for the Solve aplet if, for example, you define equations
to solve for the value of money. A number format of
Fixed2would be appropriate in this case.
Solve aplet
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Interpreting results
After Solve has returned a solution, press
in the
Numeric view for more information. You will see one of
the following three messages. Press
message.
to clear the
Message
Condition
Zero
The Solve aplet found a point where
both sides of the equation were
equal, or where the expression was
zero (a root), within the calculator's
12-digit accuracy.
Sign Reversal
Solve found two points where the
difference between the two sides of
the equation has opposite signs, but
it cannot find a point in between
where the value is zero. Similarly,
for an expression, where the value
of the expression has different signs
but is not precisely zero. This might
be because either the two points are
neighbours (they differ by one in the
twelfth digit), or the equation is not
real-valued between the two points.
Solve returns the point where the
value or difference is closer to zero.
If the equation or expression is
continuously real, this point is
Solve’s best approximation of an
actual solution.
Extremum
Solve found a point where the value
of the expression approximates a
local minimum (for positive values)
or maximum (for negative values).
This point may or may not be a
solution.
Or: Solve stopped searching at
9.99999999999E499, the largest
number the calculator can
represent.
Note that the value returned is
probably not valid.
7-6
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If Solve could not find a solution, you will see one of the
following two messages.
Message
Condition
Bad Guess(es)
The initial guess lies outside the
domain of the equation.
Therefore, the solution was not a
real number or it caused an error.
Constant?
The value of the equation is the
same at every point sampled.
H I N T
It is important to check the information relating to the
solve process. For example, the solution that the Solve
aplet finds is not a solution, but the closest that the
function gets to zero. Only by checking the information
will you know that this is the case.
The Root-Finder
at work
You can watch the process of the root-finder calculating
and searching for a root. Immediately after pressing
to start the root-finder, press any key except
You will see two intermediate guesses and, to the left, the
sign of the expression evaluated at each guess. For
example:
.
+ 2 2.219330555745
– 1 21.31111111149
You can watch as the root-finder either finds a sign
reversal or converges on a local extrema or does not
converge at all. If there is no convergence in process, you
might want to cancel the operation (press
over with a different initial guess.
) and start
Plotting to find guesses
The main reason for plotting in the Solve aplet is to help
you find initial guesses and solutions for those equations
that have difficult-to-find or multiple solutions.
Consider the equation of motion for an accelerating
body:
AT 2
X =V0T +
2
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7-7
where X is distance, V is initial velocity, T is time, and A
0
is acceleration. This is actually two equations, Y = X and
2
Y = V T + (AT ) / 2.
0
Since this equation is quadratic for T, there can be both
a positive and a negative solution. However, we are
concerned only with positive solutions, since only positive
distance makes sense.
1. Select the Solve aplet and enter the equation.
Select Solve
X
V
T
A
T
2
2. Find the solution for T (time) when X=30, V=2, and
A=4. Enter the values for X, V, and A; then highlight
the independent variable, T.
30
2
4
to highlight T
3. Use the Plot view to find an initial guess for T. First set
appropriate X and Y ranges in the Plot Setup. With
2
equation X = V x T + A x T /2, the plot will produce
two graphs: one for Y = X and one for
2
X = V x T + A x T /2. Since we have set X = 30 in
this example, one of the graphs will be Y = 30 .
Therefore, make the YRNG–5 to 35. Keep the XRNG
default of –6.5 to 6.5.
SETUP-PLOT
5
35
4. Plot the graph.
7-8
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5. Move the cursor near the positive (right-side)
intersection. This cursor value will be an initial guess
for T.
Press
until the
cursor is at the
intersection.
The two points of
intersection show that
there are two solutions for this equation. However,
only positive values for X make sense, so we want to
find the solution for the intersection on the right side
of the y-axis.
6. Return to the Numeric
view.
Note: the T-value is filled in with the position of the
cursor from the Plot view.
7. Ensure that the T value is highlighted, and solve the
equation.
Use this equation to solve for another variable, such as
velocity. How fast must a body’s initial velocity be in
order for it to travel 50 m within 3 seconds? Assume the
2
same acceleration, 4 m/s . Leave the last value of V as
the initial guess.
3
50
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7-9
Using variables in equations
You can use any of the real variable names, A to Z and
θ. Do not use variable names defined for other types,
such as M1 (a matrix variable).
Home variables
All home variables (other than those for aplet settings, like
Xminand Ytick) are global, which means they are
shared throughout the different aplets of the calculator. A
value that is assigned to a home variable anywhere
remains with that variable wherever its name is used.
Therefore, if you have defined a value for T (as in the
above example) in another aplet or even another Solve
equation, that value shows up in the Numeric view for this
Solve equation. When you then redefine the value for T
in this Solve equation, that value is applied to T in all
other contexts (until it is changed again).
This sharing allows you to work on the same problem in
different places (such as HOME and the Solve aplet)
without having to update the value whenever it is
recalculated.
H I N T
As the Solve aplet uses existing variable values, be sure
to check for existing variable values that may affect the
solve process. (You can use
CLEAR to reset all
values to zero in the Solve aplet’s Numeric view if you
wish.)
Aplet variables
Functions defined in other aplets can also be referenced
in the Solve aplet. For example, if, in the Function aplet,
2
you define F1(X)=X +10, you can enter F1(X)=50in
2
the Solve aplet to solve the equation X +10=50.
7-10
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8
Linear Solver aplet
About the Linear Solver aplet
The Linear Solver aplet allows you to solve a set of Linear
Equations. The set can contain two or three linear
equations.
In a two-equation set, each equation must be in the form
ax + by = k . In a three-equation set, each equation must
be in the form ax + by + cz = k .
You provide values for a, b, and k (and c in three-
equation sets) for each equation, and the Linear Solver
aplet will attempt to solve for x and y (and z in three-
equation sets).
The hp39gs will alert you if no solution can be found, or
if there is an infinite number of solutions.
Note that the Linear Solver aplet only has a numeric view.
Getting started with the Linear Solver aplet
The following example defines a set of three equations
and then solves for the unknown variables.
Open the
Linear Solver
aplet
1. Open the Linear Sequence aplet.
Select Linear
Solver
The Linear Equation
Solver opens.
Linear Solver aplet
8-1
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Choose the
equation set
2. If the last time you used
the Linear Solver aplet
you solved for two
equations, the two-
equation input form is
displayed (as in the
example in the
previous step). To solve a three-equation set, press
. Now the input form displays three equations.
If the three-equation input form is displayed and you want
to solve a two-equation set, press
.
In this example, we are going to solve the following
equation set:
6x + 9y + 6z = 5
7x + 10y + 8z = 10
6x + 4y = 6
Hence we need the three-equation input form.
Define and
solve the
equations
3. You define the equations you want to solve by
entering the co-efficients of each variable in each
equation and the constant term. Notice that the cursor
is immediately positioned at the co-efficient of x in the
first equation. Enter that co-efficient and press
or
.
4. The cursor moves to the next co-efficient. Enter that co-
efficient, press
or
, and continue doing
likewise until you have defined all the equations.
Note: you can enter the name of a variable for any
co-efficient or constant. Press
entering the name. The
and begin
menu key appears.
Press that key to lock alphabetic entry mode. Press it
again to cancel the lock.
Once you have entered
enough values for the
solver to be able to
generate solutions,
those solutions appear
on the display. In the
example at the right,
the solver was able to find solutions for x, y, and z as
8-2
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soon as the first co-efficient of the last equation was
entered.
As you enter each of
the remaining known
values, the solution
changes. The example
at the right shows the
final solution once all
the co-efficients and
constants are entered for the set of equations we set
out to solve.
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9
Triangle Solve aplet
About the Triangle Solver aplet
The Triangle Solver aplet allows you to determine the
length of a side of a triangle, or the angle at the vertex of
a triangle, from information you supply about the other
lengths and/or other angles.
You need to specify at least three of the six possible
values—the lengths of the three sides and the size of the
three angles—before the solver can calculate the other
values. Moreover, at least one value you specify must be
a length. For example, you could specify the lengths of
two sides and one of the angles; or you could specify two
angles and one length; or all three lengths. In each case,
the solver will calculate the remaining lengths or angles.
The hp39gs will alert you if no solution can be found, or
if you have provided insufficient data.
If you are determining the properties of a right-angled
triangle, a simpler input form is available by pressing the
menu key.
Note that the Triangle Solver aplet only has a numeric
view.
The following example solves for the unknown length of
the side of a triangle whose two known sides—of lengths
4 and 6—meet at an angle of 30 degrees.
Before you begin: You should make sure that your angle
measure mode is appropriate. If the angle information
you have is in degrees (as in this example) and your
current angle measure mode is radians or grads, change
the mode to degrees before running the solver. (See
“Mode settings” on page 1-10 for instructions.) Because
the angle measure mode is associated with the aplet, you
should start the aplet first and then change the setting.
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9-1
Open the
Triangle
Solver aplet
1. Open the Triangle Solver aplet.
Select
Triangle Solver
The Triangle Solver
aplet opens.
Note: if you have already used the Triangle Solver,
the entries and results from the previous use will still
be displayed. To start the Triangle Solver afresh, clear
the previous entries and results by pressing
CLEAR.
Choose the
triangle type
2. If the last time you used
the Triangle Solver
aplet you used the
right-angled triangle
input form, that input
form is displayed
again (as in the
example at the right). If the triangle you are
investigating is not a right-angled triangle, or you are
not sure what type it is, you should use the general
input form (illustrated in the previous step). To switch
to the general input form, press
.
If the general input form is displayed and you are
investigating a right-angled triangle, press
display the simpler input form.
to
Specify the
known values
3. Using the arrow keys, move to a field whose value
you know, enter the value and press
Repeat for each known value.
or
.
Note that the lengths of
the sides are labeled
A, B, and C, and the
angles are labeled α,
β, and δ. It is important
that you enter the
known values in the
appropriate fields. In our example, we know the
length of two sides and the angle at which those
sides meet. Hence if we specify the lengths of sides A
and B, we must enter the angle as δ (since δ is the
angle where A and B meet). If instead we entered the
9-2
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lengths as B and C, we would need to specify the
angle as α. The illustration on the display will help
you determine where to enter the known values.
Note: if you need to change the angle measure
mode, press
MODES, change the mode, and
then press
to return to the aplet.
4. Press
. The solver
calculates the values of
the unknown variables
and displays. As the
illustration at the right
shows, the length of
the unknown side in our example is 3.2296. (The
other two angles have also been calculated.)
Note: if two sides and
an adjacent acute
angle are entered and
there are two solutions,
only one will be
displayed initially.
In this case, an
menu key is displayed
(as in this example).
You press
to
display the second
solution, and
again to return to the
first solution.
Errors
No solution with
given data
If you are using the general
input form and you enter
more than 3 values, the
values might not be
consistent, that is, no
triangle could possibly have all the values you specified.
In these cases, No sol with given dataappears on
the screen.
The situation is similar if you are using the simpler input
form (for a right-angled triangle) and you enter more than
two values.
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Not enough data
If you are using the general
input form, you need to
specify at least three values
for the Triangle Solver to
be able to calculate the
remaining attributes of the
triangle. If you specify less than three, Not enough
dataappears on the screen.
If you are using the simplified input form (for a right-
angled triangle), you must specify at least two values.
In addition, you cannot specify only angles and no
lengths.
9-4
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10
Statistics aplet
About the Statistics aplet
The Statistics aplet can store up to ten data sets at one
time. It can perform one-variable or two-variable
statistical analysis of one or more sets of data.
The Statistics aplet starts with the Numeric view which is
used to enter data. The Symbolic view is used to specify
which columns contain data and which column contains
frequencies.
You can also compute statistics values in HOME and
recall the values of specific statistics variables.
The values computed in the Statistics aplet are saved in
variables, and many of these variables are listed by the
function accessible from the Statistics aplet’s
Numeric view screen.
Getting started with the Statistics aplet
The following example asks you to enter and analyze the
advertising and sales data (in the table below), compute
statistics, fit a curve to the data, and predict the effect of
more advertising on sales.
Advertising minutes
(independent, x)
Resulting Sales ($)
(dependent, y)
2
1
3
5
5
4
1400
920
1100
2265
2890
2200
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10-1
Open the
Statistics aplet
1. Open the Statistics aplet and clear existing data by
pressing
.
Select Statistics
The Statistics aplet
starts in the Numerical
view.
1VAR/2VAR
menu key label
At any time the Statistics aplet is configured for only
one of two types of statistical explorations: one-
variable (
) or two-variable (
). The 5th
menu key label in the Numeric view toggles between
these two options and shows the current option.
2. Select
.
You need to select
because in this example
we are analyzing a dataset comprising two
variables: advertising minutes and resulting sales.
Enter data
3. Enter the data into the columns.
2
3
5
1
5
4
to move to the next
column
1400
1100
2890
920
2265
2200
10-2
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Choose fit and
data columns
4. Select a fit in the Symbolic setup view.
SETUP-SYMB
Select Linear
You can create up to five explorations of two-variable
data, named S1to S5. In this example, we will create
just one: S1.
5. Specify the columns that hold the data you want to
analyze.
You could have entered
your data into columns
other than C1and C2.
Explore statistics 6. Find the mean advertising time (MEANX) and the
mean sales (MEANY).
MEANXis 3.3 minutes
and MEANYis about
$1796.
7. Scroll down to display the value for the correlation
coefficient (CORR). The CORRvalue indicates how
well the linear model fits the data.
9 times
The value is .8995.
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10-3
Setup plot
8. Change the plotting range to ensure all the data
points are plotted (and select a different point mark, if
you wish).
SETUP-PLOT
7
100
4000
Plot the graph
9. Plot the graph.
Draw the
regression curve
10.Draw the regression curve (a curve to fit the data
points).
This draws the
regression line for the
best linear fit.
Display the
equation for
best linear fit
11.Return to the Symbolic view.
12.Display the equation for the best linear fit.
to move to the
FIT1field
The full FIT1
expression is shown.
The slope (m) is 425.875. The y-intercept (b) is
376.25.
10-4
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Predict values
13.To find the predicted sales figure if advertising were
to go up to 6 minutes:
S (to highlight
Stat-Two)
(to highlight
PREDY)
6
14.Return to the Plot view.
15.Jump to the indicated point on the regression line.
6
Observe the predicted
y-value in the left
bottom corner of the
screen.
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Entering and editing statistical data
The Numeric view (
) is used to enter data into the
Statistics aplet. Each column represents a variable named
C0to C9. After entering the data, you must define the
data set in the Symbolic view (
).
H I N T
A data column must have at least four data points to
provide valid two-variable statistics, or two data points
for one-variable statistics.
You can also store statistical data values by copying lists
from HOME into Statistics data columns. For example, in
HOME, L1
C1stores a copy of the list L1into the
data-column variable C1.
Statistics aplet’s NUM view keys
The Statistics aplet’s Numeric view keys are:
Key
Meaning
Copies the highlighted item into the
edit line.
Inserts a zero value above the
highlighted cell.
Sorts the specified independent
data column in ascending or
descending order, and rearranges
a specified dependent (or
frequency) data column
accordingly.
Switches between larger and
smaller font sizes.
A toggle switch to select one-
variable or two-variable statistics.
This setting affects the statistical
calculations and plots. The label
indicates which setting is current.
Computes descriptive statistics for
each data set specified in Symbolic
view.
10-6
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Key
Meaning (Continued)
Deletes the currently highlighted
value.
CLEAR
Clears the current column or all
columns of data. Pregss
CLEAR to display a menu list,
then select the current column or all
columns option, and press
.
Moves to the first or last row, or first
cursor key or last column.
Example
You are measuring the height of students in a classroom
to find the mean height. The first five students have the
following measurements 160cm, 165cm, 170cm,
175cm, 180cm.
1. Open the Statistics aplet.
Select
Statistics
2. Enter the measurement
data.
160
165
170
175
180
3. Find the mean of the
sample.
Ensure the
/
menu key label
. Press
reads
to see the
statistics calculated from the sample data in C1.
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Note that the title of the
column of statistics is
H1. There are 5 data
set definitions available
for one-variable
statistics: H1–H5. If
data is entered in C1, H1is automatically set to use
C1for data, and the frequency of each data point is
set to 1. You can select other columns of data from
the Statistics Symbolic setup view.
4. Press
to close the
statistics window and
press
key to see
the data set definitions.
The first column
indicates the associated column of data for each data
set definition, and the second column indicates the
constant frequency, or the column that holds the
frequencies.
The keys you can use from this window are:
Key
Meaning
Copies the column variable (or
variable expression) to the edit line
for editing. Press
when done.
Checks/unchecks the current data
set. Only the checkmarked data
set(s) are computed and plotted.
or
Typing aid for the column variables
(
) or for the Fit expressions ( ).
Displays the current variable
expression in standard
mathematical form. Press
done.
when
Evaluates the variables in the
highlighted column (C1, etc.)
expression.
10-8
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Key
Meaning (Continued)
Displays the menu for entering
variable names or contents of
variables.
Displays the menu for entering math
operations.
Deletes the highlighted variable or
the current character in the edit line.
CLEAR
Resets default specifications for the
data sets or clears the edit line (if it
was active).
Note: If
CLEAR is used the
data sets will need to be selected
again before re-use.
To continue our example, suppose that the heights of the
rest of the students in the class are measured, but each
one is rounded to the nearest of the five values first
recorded. Instead of entering all the new data in C1, we
shall simply add another column, C2, that holds the
frequencies of our five data points in C1.
Height
(cm)
Frequency
160
165
170
175
180
5
3
8
2
1
5. Move the highlight bar
into the right column of
the H1definition and
replace the frequency
value of 1 with the
name C2.
2
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10-9
6. Return to the numeric view.
7. Enter the frequency data shown in the above table.
5
3
8
2
1
8. Display the computed
statistics.
The mean height is
approximately
167.63cm.
9. Setup a histogram plot for the data.
SETUP-PLOT
Enter set up information
appropriate to your
data.
10.Plot a histogram of the
data.
Save data
The data that you enter is automatically saved. When you
are finished entering data values, you can press a key for
another Statistics view (like
another aplet or HOME.
), or you can switch to
Edit a data set
In the Numeric view of the Statistics aplet, highlight the
data value to change. Type a new value and
press
, or press
to copy the value to the edit
after modifying the
line for modification. Press
value on the edit line.
10-10
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Delete data
Insert data
•
•
To delete a single data item, highlight it and press
. The values below the deleted cell will scroll up
one row.
To delete a column of data, highlight an entry in that
column and press
name.
CLEAR. Select the column
•
To delete all columns of data, press
CLEAR.
Select All columns.
Highlight the entry following the point of insertion. Press
, then enter a number. It will write over the zero that
was inserted.
Sort data
values
1. In Numeric view, highlight the column you want to
sort, and press
.
2. Specify the Sort Order. You can choose either
Ascendingor Descending.
3. Specify the INDEPENDENTand DEPENDENTdata
columns. Sorting is by the independent column. For
instance, if Age is C1and Income is C2and you
want to sort by Income, then you make C2the
independent column for the sorting and C1the
dependent column.
–
To sort just one column, choose None for the
dependent column.
–
For one-variable statistics with two data columns,
specify the frequency column as the dependent
column.
4. Press
.
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Defining a regression model
The Symbolic view includes an expression (Fit1 through
Fit5) that defines the regression model, or “fit”, to use for
the regression analysis of each two-variable data set.
There are three ways to select a regression model:
•
•
•
Accept the default option to fit the data to a straight
line.
Select one of the available fit options in Symbolic
Setup view.
Enter your own mathematical expression in Symbolic
view. This expression will be plotted, but it will not be
fitted to the data points.
Angle Setting
You can ignore the angle measurement mode unless your
Fit definition (in Symbolic view) involves a trigonometric
function. In this case, you should specify in the mode
screen whether the trigonometric units are to be
interpreted in degrees, radians, or grads.
To choose the fit 1. In Numeric view, make sure
is set.
2. Press
SETUP-SYMB to display the Symbolic Setup
view. Highlight the Fit number (S1FITto S5FIT) you
want to define.
3. Press
and select from the list. Press
when
done. The regression formula for the fit is displayed in
Symbolic view.
Fit models
Ten fit models are available:
Fit model
Meaning
Linear
(Default.) Fits the data to a
straight line, y = mx+b. Uses a
least-squares fit.
Logarithmic
Exponential
Power
Fits to a logarithmic curve,
y = m lnx + b.
Fits to an exponential curve,
mx
y = be .
m
Fits to a power curve, y = bx .
10-12
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Fit model
Meaning (Continued)
Quadratic
Fits to a quadratic curve,
2
y = ax +bx+c. Needs at least
three points.
Cubic
Fits to a cubic curve,
3
2
y = ax +bx +cx+d. Needs at least
four points.
Logistic
Fits to a logistic curve,
L
--------------------------
y =
,
1 + ae(–bx)
where L is the saturation value for
growth. You can store a positive
real value in L, or—if L=0—let L
be computed automatically.
Exponent
Fits to an exponent curve,
y = abx .
Trigonometric
Fits to a trigonometric curve,
y = a ⋅ sin(bx + c) + d . Needs at
least three points.
User Defined
Define your own expression (in
Symbolic view.)
To define your
own fit
1. In Numeric view, make sure
2. Display the Symbolic view.
is set.
3. Highlight the Fit expression (Fit1, etc.) for the
desired data set.
4. Type in an expression and press
.
The independent variable must be X, and the
expression must not contain any unknown variables.
Example:1.5 × cosx + 0.3 × sinx .
This automatically changes the Fit type (S1FIT, etc.) in
the Symbolic Setup view to User Defined.
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Computed statistics
One-variable
Statistic
Definition
NΣ
Number of data points.
TOTΣ
Sum of data values (with their
frequencies).
MEANΣ
PVARΣ
SVARΣ
PSDEV
Mean value of data set.
Population variance of data set.
Sample variance of data set.
Population standard deviation of
data set.
SSDEV
Sample standard deviation of data
set.
MINΣ
Minimum data value in data set.
Q1
First quartile: median of values to
left of median.
MEDIAN
Q3
Median value of data set.
Third quartile: median of values to
right of median.
MAXΣ
Maximum data value in data set.
When the data set contains an odd number of values, the
data set’s median value is not used when calculating Q1
and Q3 in the table above. For example, for the following
data set:
{3,5,7,8,15,16,17}
only the first three items, 3, 5, and 7 are used to calculate
Q1, and only the last three terms, 15, 16, and 17 are
used to calculate Q3.
10-14
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Two-variable
Statistic
MEANX
ΣX
Definition
Mean of x- (independent) values.
Sum of x-values.
2
ΣX2
Sum of x -values.
MEANY
ΣY
Mean of y- (dependent) values.
Sum of y-values.
2
ΣY2
Sum of y -values.
ΣXY
Sum of each xy.
SCOV
Sample covariance of independent
and dependent data columns.
PCOV
CORR
Population covariance of
independent and dependent data
columns
Correlation coefficient of the
independent and dependent data
columns for a linear fit only
(regardless of the Fit chosen).
Returns a value from 0 to 1, where
1 is the best fit.
RELERR
The relative error for the selected
fit. Provides a measure of accuracy
for the fit.
Plotting
You can plot:
•
•
•
histograms (
)
box-and-whisker plots (
scatter plots ( ).
)
Once you have entered your data (
data set ( ), and defined your Fit model for two-
variable statistics ( SETUP-SYMB), you can plot your
), defined your
data. You can plot up to five scatter or box-and-whisker
plots at a time. You can plot only one histogram at a time.
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To plot statistical
data
1. In Symbolic view (
sets you want to plot.
), select (
) the data
2. For one-variable data (
), select the plot type in
Plot Setup (
SETUP-PLOT). Highlight STATPLOT,
press
, select either Histogramor
BoxWhisker, and press
.
3. For any plot, but especially for a histogram, adjust the
plotting scale and range in the Plot Setup view. If you
find histogram bars too fat or too thin, you can adjust
them by adjusting the HWIDTHsetting.
4. Press
. If you have not adjusted the Plot Setup
select Auto Scale
yourself, you can try
.
Auto Scale can be relied upon to give a good starting
scale which can then be adjusted in the Plot Setup view.
Plot types
Histogram
One-variable statistics.
The numbers below the plot
mean that the current bar
(where the cursor is) starts at
0 and ends at 2 (not
including 2), and the
frequency for this column, (that is, the number of data
elements that fall between 0 and 2) is 1. You can see
information about the next bar by pressing the
key.
Box and
Whisker Plot
One-variable statistics.
The left whisker marks the
minimum data value. The
box marks the first quartile,
the median (where the cursor
is), and the third quartile.
The right whisker marks the maximum data value. The
numbers below the plot mean that this column has a
median of 13.
10-16
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Scatter Plot
Two-variable statistics.
The numbers below the plot
indicate that the cursor is at
the first data point for S2, at
(1, 6). Press
to move to
the next data point and
display information about it.
To connect the data points as
they are plotted, checkmark
CONNECTin the second
page of the Plot Setup. This is
not a regression curve.
Fitting a curve to 2VAR data
In the Plot view, press
. This draws a curve to fit the
checked two-variable data set(s). See “To choose the fit”
on page 10-12.
The expression in Fit2
shows that the
slope=1.98082191781
and the y-
intercept=2.2657.
Correlation
coefficient
The correlation coefficient is stored in the CORRvariable.
It is a measure of fit to a linear curve only. Regardless of
the Fit model you have chosen, CORR relates to the linear
model.
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Relative Error
The relative error is a measure of the error between
predicted values and actual values based on the specified
Fit. A smaller number means a better fit.
The relative error is stored in a variable named RELERR.
The relative error provides a measure of fit accuracy for
all fits, and it does depend on the Fit model you have
chosen.
H I N T
In order to access the CORRand RELERRvariables after
you plot a set of statistics, you must press
to display the
the numeric view and then
correlation values. The values are stored in the variables
when you access the Symbolic view.
Setting up the plot (Plot setup view)
The Plot Setup view (
SETUP-PLOT) sets most of the
same plotting parameters as it does for the other built-in
aplets.
See “About the Plot view” on page 2-5. Settings unique
to the Statistics aplet are as follows:
Plot type (1VAR)
Histogram width
Histogram range
STATPLOTenables you to specify either a histogram or
a box-and-whisker plot for one-variable statistics (when
is set). Press
to change the highlighted
setting
HWIDTHenables you to specify the width of a histogram
bar. This determines how many bars will fit in the display,
as well as how the data is distributed (how many values
each bar represents).
HRNGenables you to specify the range of values for a set
of histogram bars. The range runs from the left edge of the
leftmost bar to the right edge of the rightmost bar. You
can limit the range to exclude any values you suspect are
outliers.
Plotting mark
(2VAR)
S1MARKthrough S5MARKenables you to specify one of
five symbols to use to plot each data set. Press
change the highlighted setting.
to
Connected points
(2VAR)
CONNECT(on the second page), when checkmarked,
connects the data points as they are plotted. The resulting
line is not the regression curve. The order of plotting is
according to the ascending order of independent values.
10-18
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For instance, the data set (1,1), (3,9), (4,16), (2,4) would
be plotted and traced in the order (1,1), (2,4), (3,9),
(4,16).
Trouble-shooting a plot
If you have problems plotting, check that you have the
following:
•
•
•
The correct
view).
or
menu label on (Numeric
The correct fit (regression model), if the data set is
two-variable.
Only the data sets to compute or plot are
checkmarked (Symbolic view).
•
The correct plotting range. Try using
Auto
Scale (instead of ), or adjust the plotting
parameters (in Plot Setup) for the ranges of the axes
and the width of histogram bars (HWIDTH).
In
mode, ensure that both paired columns contain
data, and that they are the same length.
In
mode, ensure that a paired column of frequency
values is the same length as the data column that it refers
to.
Exploring the graph
The Plot view has menu keys for zooming, tracing, and
coordinate display. There are also scaling options under
. These options are described in“Exploring the
graph” on page 2-7.
Statistics aplet’s PLOT view keys
Key
Meaning
CLEAR
Erases the plot.
Offers additional pre-defined views
for splitting the screen, overlaying
plots, and autoscaling the axes.
Moves cursor to far left or far right.
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10-19
Key
Meaning (Continued)
Displays ZOOM menu.
Turns trace mode on/off. The white
box appears next to the option when
Trace mode is active.
Turns fit mode on or off. Turning
on draws a curve to fit the data points
according to the current regression
model.
(2var
Enables you to specify a value on the
statistics only) line of best fit to jump to or a data
point number to jump to.
Displays the equation of the
regression curve.
Hides and displays the menu key
labels. When the labels are hidden,
any menu key displays the (x,y)
coordinates. Pressing
redisplays the menu labels.
Calculating predicted values
The functions PREDXand PREDYestimate (predict) values
for X or Y given a hypothetical value for the other. The
estimation is made based on the curve that has been
calculated to fit the data according to the specified fit.
Find predicted
values
1. In Plot view, draw the regression curve for the data
set.
2. Press
3. Press
to move to the regression curve.
and enter the value of X. The cursor
jumps to the specified point on the curve and the
coordinate display shows X and the predicted value
of Y.
In HOME:
•
Enter PREDX(y-value)
to find the predicted
value for the independent variable given a
hypothetical dependent value.
10-20
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•
Enter PREDY(x-value) to find the predicted value of the
dependent variable given a hypothetical independent
variable.
You can type PREDXand PREDYinto the edit line, or you
can copy these function names from the MATH menu
under the Stat-Two category.
H I N T
In cases where more than one fit curve is displayed, the
PREDY function uses the most recently calculated curve. In
order to avoid errors with this function, uncheck all fits
except the one that you want to work with, or use the Plot
View method.
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11
Inference aplet
About the Inference aplet
The Inference capabilities include calculation of
confidence intervals and hypothesis tests based on the
Normal Z-distribution or Student’s t-distribution.
Based on the statistics from one or two samples, you can
test hypotheses and find confidence intervals for the
following quantities:
•
•
•
•
mean
proportion
difference between two means
difference between two proportions
Example data
When you first access an input form for an Inference test,
by default, the input form contains example data. This
example data is designed to return meaningful results that
relate to the test. It is useful for gaining an understanding
of what the test does, and for demonstrating the test. The
calculator’s on-line help provides a description of what
the example data represents.
Getting started with the Inference aplet
This example describes the Inference aplet’s options and
functionality by stepping you through an example using
the example data for the Z-Test on 1 mean.
Open the
Inference aplet
1. Open the Inference aplet.
Select Inference
.
The Inference aplet
opens in the Symbolic
view.
Inference aplet
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Inference aplet’s SYMB view keys
The table below summarizes the options available in
Symbolic view.
Hypothesis
Tests
Confidence Intervals
Z: 1 μ, the Z-Test
on 1 mean
Z-Int: 1 μ, the confidence
interval for 1 mean, based on
the Normal distribution
Z: μ – μ , the
Z-Int: μ – μ , the confidence
1
2
1
2
Z-Test on the
difference of two
means
interval for the difference of
two means, based on the
Normal distribution
Z: 1 π, the Z-Test
on 1 proportion
Z-Int: 1 π, the confidence
interval for 1 proportion,
based on the Normal
distribution
Z: π1 – π2, the
Z-Test on the
difference in two
proportions
Z-Int: π1 – π2, the confidence
interval for the difference of
two proportions, based on the
Normal distribution
T: 1 μ, the T-Test on
1 mean
T-Int: 1 μ, the confidence
interval for 1 mean, based on
the Student’s t-distribution
T: μ – μ , the T-
T-Int: μ – μ , the confidence
1
2
1
2
Test on the
difference of two
means
interval for the difference of
two means, based on the
Student’s t-distribution
If you choose one of the hypothesis tests, you can choose
the alternative hypothesis to test against the null
hypothesis. For each test, there are three possible choices
for an alternative hypothesis based on a quantitative
comparison of two quantities. The null hypothesis is
always that the two quantities are equal.Thus, the
alternative hypotheses cover the various cases for the two
quantities being unequal: <, >, and ≠.
In this section, we will use the example data for the Z-Test
on 1 mean to illustrate how the aplet works and what
features the various views present.
11-2
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Select the
inferential
method
2. Select the HypothesisTest inferential method.
Select HYPOTH TEST
3. Define the type of test.
Z–Test:1 μ
4. Select an alternative hypothesis.
μ< μ0
Enter data
5. Enter the sample statistics and population
parameters.
setup-NUM
The table below lists the fields in this view for our current
Z-Test:1 μ example.
Field
Definition
name
μ0
Assumed population mean
Population standard deviation
Sample mean
σ
x
n
α
Sample size
Alpha level for the test
Inference aplet
11-3
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By default, each field already contains a value.
These values constitute the example database and
are explained in the
feature of this aplet.
Display on-line
help
6. To display the on-line
help, press
7. To close the on-line help,
press
.
Display test
results in
numeric format
8. Display the test results in numeric format.
The test distribution value
and its associated
probability are
displayed, along with
the critical value(s) of the test and the associated
critical value(s) of the statistic.
Note: You can access the on-line help in Numeric
view.
Plot test results
9. Display a graphic view of the test results.
Horizontal axes are
presented for both the
distribution variable and
the test statistic. A
generic bell curve represents the probability
distribution function. Vertical lines mark the critical
value(s) of the test, as well as the value of the test
R
statistic. The rejection region is marked
and the
test numeric results are displayed between the
horizontal axes.
Importing sample statistics from the Statistics aplet
The Inference aplet supports the calculation of confidence
intervals and the testing of hypotheses based on data in
the Statistics aplet. Computed statistics for a sample of
data in a column in any Statistics-based aplet can be
imported for use in the Inference aplet. The following
example illustrates the process.
11-4
Inference aplet
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A calculator produces the following 6 random numbers:
0.529, 0.295, 0.952, 0.259, 0.925, and 0.592
Open the
Statistics aplet
1. Open the Statistics aplet and reset the current
settings.
Select
Statistics
The Statistics aplet opens in the Numeric view.
Enter data
2. In the C1 column, enter the random numbers
produced by the calculator.
529
295
952
259
925
592
H I N T
If the Decimal Mark setting in the Modes input form
(
modes) is set to Comma, use
instead of
.
3. If necessary, select 1-variable statistics. Do this by
pressing the fifth menu key until
as its menu label.
is displayed
Calculate
statistics
4. Calculate statistics.
The mean of 0.592
seems a little large
compared to the
expected value of 0.5. To see if the difference is
statistically significant, we will use the statistics
computed here to construct a confidence interval for
the true mean of the population of random numbers
and see whether or not this interval contains 0.5.
5. Press
to close the computed statistics window.
Inference aplet
11-5
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Open Inference
aplet
6. Open the Inference aplet and clear current settings.
Select
Inference
Select inference
method and
type
7. Select an inference method.
Select CONF INTERVAL
8. Select a distribution statistic type.
Select T-Int: 1μ
Set up the
interval
calculation
9. Set up the interval calculation. Note: The default
values are derived from sample data from the on-line
help example.
Setup-NUM
11-6
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Import the data
10.Import the data from the Statistics aplet. Note: The
data from C1 is displayed by default.
Note: Press
to see
the statistics before
importing them into the
Numeric Setup view.
Also, if there is more than one aplet based on the
Statistics aplet, you are prompted to choose one.
11.Specify a 90%
confidence interval in the C: field.
to move to
the C: field
0.9
DisplayNumeric 12.Display the confidence interval in the Numeric view.
Note: The interval setting is 0.5.
view
Display Plot
view
13.Display the confidence interval in the Plot view.
You can see, from the
second text row, that the
mean is contained within the 90% confidence
interval (CI) of 0.3469814 to 0.8370186.
Note: The graph is a simple, generic bell-curve. It is
not meant to accurately represent the t-distribution
with 5 degrees of freedom.
Inference aplet
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Hypothesis tests
You use hypothesis tests to test the validity of hypotheses
that relate to the statistical parameters of one or two
populations. The tests are based on statistics of samples
of the populations.
The HP 39gs hypothesis tests use the Normal
Z-distribution or Student’s t-distribution to calculate
probabilities.
One-Sample Z-Test
Menu name
Z-Test: 1 μ
On the basis of statistics from a single sample, the
One-Sample Z-Test measures the strength of the evidence
for a selected hypothesis against the null hypothesis. The
null hypothesis is that the population mean equals a
specified value Η : μ = μ .
0
0
You select one of the following alternative hypotheses
against which to test the null hypothesis:
H1:μ1 < μ2
H1:μ1 > μ2
H1:μ1 ≠ μ2
Inputs
The inputs are:
Field name
Definition
x
n
Sample mean.
Sample size.
μ
Hypothetical population mean.
Population standard deviation.
Significance level.
0
σ
α
11-8
Inference aplet
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Results
The results are:
Result
Test Z
Prob
Description
Z-test statistic.
Probability associated with the
Z-Test statistic.
Critical Z
Boundary values of Z
associated with the α level that
you supplied.
Boundary values of x required
by the α value that you
supplied.
Critical x
Two-Sample Z-Test
Menu name
Z-Test: μ1–μ2
On the basis of two samples, each from a separate
population, this test measures the strength of the evidence
for a selected hypothesis against the null hypothesis. The
null hypothesis is that the mean of the two populations are
equal (H : μ1= μ2).
0
You select one of the following alternative hypotheses
against which to test the null hypothesis:
H1:μ1 < μ2
H1:μ1 > μ2
H1:μ1 ≠ μ2
Inputs
The inputs are:
Field name
Definition
Sample 1 mean.
x1
Sample 2 mean.
x2
n1
n2
σ1
Sample 1 size.
Sample 2 size.
Population 1 standard
deviation.
Inference aplet
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Field name
Definition (Continued)
σ2
Population 2 standard
deviation.
α
Significance level.
Results
The results are:
Result
Test Z
Prob
Description
Z-Test statistic.
Probability associated with the
Z-Test statistic.
Critical Z
Boundary value of Z
associated with the α level that
you supplied.
One-Proportion Z-Test
Menu name
Z-Test: 1π
On the basis of statistics from a single sample, this test
measures the strength of the evidence for a selected
hypothesis against the null hypothesis. The null hypothesis
is that the proportion of successes in the two populations
is equal: H :π =π
0
0
You select one of the following alternative hypotheses
against which to test the null hypothesis:
H1:π < π0
H1:π > π0
H1:π ≠ π0
11-10
Inference aplet
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Inputs
The inputs are:
Field name
Definition
x
n
Number of successes in the sample.
Sample size.
π
Population proportion of successes.
Significance level.
0
α
Results
The results are:
Result
Test P
Test Z
Prob
Description
Proportion of successes in the sample.
Z-Test statistic.
Probability associated with the Z-Test
statistic.
Critical Z
Boundary value of Z associated with
the level you supplied.
Two-Proportion Z-Test
Menu name
Z-Test: π1 – π2
On the basis of statistics from two samples, each from a
different population, the Two-Proportion Z-Test measures
the strength of the evidence for a selected hypothesis
against the null hypothesis. The null hypothesis is that the
proportion of successes in the two populations is equal
H0: π = π .
1
2
You select one of the following alternative hypotheses
against which to test the null hypothesis:
H1:π1 < π2
H1:π1 > π2
H1:π1 ≠ π2
Inference aplet
11-11
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Inputs
The inputs are:
Field name
Definition
X1
X2
n1
n2
α
Sample 1 mean.
Sample 2 mean.
Sample 1 size.
Sample 2 size.
Significance level.
Results
The results are:
Result
Description
Test π1–π2
Difference between the
proportions of successes in the
two samples.
Test Z
Prob
Z-Test statistic.
Probability associated with the
Z-Test statistic.
Critical Z
Boundary values of Z
associated with the α level that
you supplied.
One-Sample T-Test
Menu name
T-Test: 1 μ
The One-sample T-Test is used when the population
standard deviation is not known. On the basis of statistics
from a single sample, this test measures the strength of the
evidence for a selected hypothesis against the null
hypothesis. The null hypothesis is that the sample mean
has some assumed value,
Η
:μ = μ
0
0
You select one of the following alternative hypotheses
against which to test the null hypothesis:
H1:μ < μ0
H1:μ > μ0
H1:μ ≠ μ0
11-12
Inference aplet
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Inputs
The inputs are:
Field name
Definition
Sample mean.
x
Sx
n
Sample standard deviation.
Sample size.
μ0
α
Hypothetical population mean.
Significance level.
Results
The results are:
Result
Test T
Prob
Description
T-Test statistic.
Probability associated with the
T-Test statistic.
Critical T
Boundary value of T associated
with the α level that you
supplied.
Boundary value of x required
by the α value that you
supplied.
Critical x
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Two-Sample T-Test
Menu name
T-Test: μ1 – μ2
The Two-sample T-Test is used when the population
standard deviation is not known. On the basis of statistics
from two samples, each sample from a different
population, this test measures the strength of the evidence
for a selected hypothesis against the null hypothesis. The
null hypothesis is that the two populations means are
equal H : μ = μ .
0
1
2
You select one of the following alternative hypotheses
against which to test the null hypothesis
H1:μ1 < μ2
H1:μ1 > μ2
H1:μ1 ≠ μ2
Inputs
The inputs are:
Field
name
Definition
Sample 1 mean.
Sample 2 mean.
x1
x2
S1
S2
n1
n2
α
Sample 1 standard deviation.
Sample 2 standard deviation.
Sample 1 size.
Sample 2 size.
Significance level.
_Pooled? Check this option to pool samples
based on their standard deviations.
11-14
Inference aplet
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Results
The results are:
Result
Test T
Prob
Description
T-Test statistic.
Probability associated with the T-Test
statistic.
Critical T
Boundary values of T associated with
the α level that you supplied.
Confidence intervals
The confidence interval calculations that the HP 39gs can
perform are based on the Normal Z-distribution or
Student’s t-distribution.
One-Sample Z-Interval
Menu name
Z-INT: μ 1
This option uses the Normal Z-distribution to calculate a
confidence interval for m, the true mean of a population,
when the true population standard deviation, s, is known.
Inputs
The inputs are:
Field
Definition
name
Sample mean.
x
σ
n
C
Population standard deviation.
Sample size.
Confidence level.
Inference aplet
11-15
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Results
The results are:
Result
Critical Z
μ min
Description
Critical value for Z.
Lower bound for μ.
Upper bound for μ.
μ max
Two-Sample Z-Interval
Menu name
Z-INT: μ1– μ2
This option uses the Normal Z-distribution to calculate a
confidence interval for the difference between the means
of two populations, μ –μ , when the population standard
1
2
deviations, σ and σ , are known.
1
2
Inputs
The inputs are:
Field
Definition
name
Sample 1 mean.
Sample 2 mean.
x1
x2
n1
n2
σ1
σ2
C
Sample 1 size.
Sample 2 size.
Population 1 standard deviation.
Population 2 standard deviation.
Confidence level.
Results
The results are:
Result
Description
Critical Z
Critical value for Z.
Lower bound for μ – μ .
Δ μ Min
Δ μ Max
1
2
Upper bound for μ – μ .
1
2
11-16
Inference aplet
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One-Proportion Z-Interval
Menu name
Z-INT: 1 π
This option uses the Normal Z-distribution to calculate a
confidence interval for the proportion of successes in a
population for the case in which a sample of size, n, has
a number of successes, x.
Inputs
The inputs are:
Field
Definition
name
x
n
C
Sample success count.
Sample size.
Confidence level.
Results
The results are:
Result
Critical Z
π Min
Description
Critical value for Z.
Lower bound for π.
Upper bound for π.
π Max
Two-Proportion Z-Interval
Menu name
Z-INT: π1 – π2
This option uses the Normal Z-distribution to calculate a
confidence interval for the difference between the
proportions of successes in two populations.
Inputs
The inputs are:
Field
Definition
name
Sample 1 success count.
Sample 2 success count.
x1
x2
Inference aplet
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Field
Definition (Continued)
name
n1
n2
C
Sample 1 size.
Sample 2 size.
Confidence level.
Results
The results are:
Result
Description
Critical Z
Critical value for Z.
Lower bound for the difference between
the proportions of successes.
Δ π Min
Upper bound for the difference between
the proportions of successes.
Δ π Max
One-Sample T-Interval
Menu name
T-INT: 1 μ
This option uses the Student’s t-distribution to calculate a
confidence interval for m, the true mean of a population,
for the case in which the true population standard
deviation, s, is unknown.
Inputs
The inputs are:
Field
Definition
name
Sample mean.
x1
Sx
n
Sample standard deviation.
Sample size.
C
Confidence level.
11-18
Inference aplet
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Results
The results are:
Result
Critical T
μ Min
Description
Critical value for T.
Lower bound for μ.
Upper bound for μ.
μ Max
Two-Sample T-Interval
Menu name
T-INT: μ1 – μ2
This option uses the Student’s t-distribution to calculate a
confidence interval for the difference between the means
of two populations, μ1 – μ2, when the population
standard deviations, s1and s2, are unknown.
Inputs
The inputs are:
Field
Definition
name
Sample 1 mean.
Sample 2 mean.
x1
x2
s1
Sample 1 standard deviation.
Sample 2 standard deviation.
Sample 1 size.
s2
n1
n2
Sample 2 size.
C
Confidence level.
_Pooled
Whether or not to pool the samples
based on their standard deviations.
Inference aplet
11-19
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Results
The results are:
Result
Description
Critical T
Critical value for T.
Lower bound for μ – μ .
Δ μ Min
Δ μ Max
1
2
Upper bound for μ – μ .
1
2
11-20
Inference aplet
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12
Using the Finance Solver
The Finance Solver, or Finance aplet, is available by
using the APLET key in your calculator. Use the up and
down arrow keys to select the Finance aplet. Your screen
should look as follows:
Press the
key or the
soft menu key to
activate the aplet. The resulting screen shows the different
elements involved in the solution of financial problems
with your HP 39gs calculator.
Background information on and applications of financial
calculations are provided next.
Background
The Finance Solver application provides you with the
ability of solving time-value-of-money (TVM) and
amortization problems. These problems can be used for
calculations involving compound interest applications as
well as amortization tables.
Compound interest is the process by which earned
interest on a given principal amount is added to the
principal at specified compounding periods, and then the
Using the Finance Solver
12-1
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combined amount earns interest at a certain rate.
Financial calculations involving compound interest
include savings accounts, mortgages, pension funds,
leases, and annuities.
Time Value of Money (TVM) calculations, as the name
implies, make use of the notion that a dollar today will be
worth more than a dollar sometime in the future. A dollar
today can be invested at a certain interest rate and
generate a return that the same dollar in the future cannot.
This TVM principle underlies the notion of interest rates,
compound interest and rates of return.
TVM transactions can be represented by using cash flow
diagrams. A cash flow diagram is a time line divided into
equal segments representing the compounding periods.
Arrows represent the cash flows, which could be positive
(upward arrows) or negative (downward arrows),
depending on the point of view of the lender or borrower.
The following cash flow diagram shows a loan from a
borrower's point of view:
Present value (PV)
(Loan)
Money
Equal periods
received is
a positive
number
1
2
3
4
5
(PMT)
Payment Payment Payment
(PMT) (PMT) (PMT)
Payment
(PMT)
Money
Future value
(FV)
paid out is
a negative
number
Equal payments
On the other hand, the following cash flow diagram
shows a load from the lender's point of view:
Equal payments
FV
PMT
PMT
PMT PMT
4
PMT
1
2
3
5
Loan
}
Equal periods
PV
In addition, cash flow diagrams specify when payments
occur relative to the compounding periods: at the
beginning of each period or at the end. The Finance
Solver application provides both of these payment
modes: Begin mode and End mode. The following cash
12-2
Using the Finance Solver
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flow diagram shows lease payments at the beginning of
each period.
PV
Capitalized
value of
lease
}
1
2
3
4
5
PMT
PMT PMT PMT
PMT
FV
The following cash flow diagram shows deposits into an
account at the end of each period.
FV
1
2
3
4
5
PMT PMT PMT PMT
PMT
PV
As these cash-flow diagrams imply, there are five TVM
variables:
N
The total number of compounding periods
or payments.
I%YR
The nominal annual interest rate (or
investment rate). This rate is divided by
the number of payments per year (P/YR)
to compute the nominal interest rate per
compounding period -- which is the
interest rate actually used in TVM
calculations.
The present value of the initial cash flow.
To a lender or borrower, PV is the amount
of the loan; to an investor, PV is the initial
investment. PV always occurs at the
beginning of the first period.
PV
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12-3
The periodic payment amount. The
payments are the same amount each
period and the TVM calculation assumes
that no payments are skipped. Payments
can occur at the beginning or the end of
each compounding period -- an option
you control by setting the Payment mode
to Beg or End.
PMT
The future value of the transaction: the
amount of the final cash flow or the
compounded value of the series of
previous cash flows. For a loan, this is the
size of the final balloon payment (beyond
any regular payment due). For an
investment this is the cash value of an
investment at the end of the investment
period.
FV
Performing TVM calculations
1. Launch the Financial Solver as indicated at the
beginning of this section.
2. Use the arrow keys to highlight the different fields and
enter the known variables in the TVM calculations,
pressing the
soft-menu key after entering each
known value. Be sure that values are entered for at
least four of the five TVM variables (namely, N, I%YR,
PV, PMT, and FV).
3. If necessary, enter a different value for P/YR (default
value is 12, i.e., monthly payments).
4. Press the key
to change the Payment mode (Beg
or End) as required.
5. Use the arrow keys to highlight the TVM variable you
wish to solve for and press the
soft-menu key.
12-4
Using the Finance Solver
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Example 1 - Loan calculations
Suppose you finance the purchase of a car with a 5-year
loan at 5.5% annual interest, compounded monthly. The
purchase price of the car is $19,500, and the down
payment is $3,000. What are the required monthly
payments? What is the largest loan you can afford if your
maximum monthly payment is $300? Assume that the
payments start at the end of the first period.
Solution. The following cash flow diagram illustrates the
loan calculations:
FV = 0
l%YR = 5.5
PV = $16,500
N = 5 x 12 = 60
P/YR = 12; End mode
1
2
59
60
PMT = ?
Start the Finance Solver, selecting P/YR = 12 and End
payment option.
•
Enter the known TVM variables as shown in the
diagram above. Your input form should look as
follows:
•
•
Highlighting the PMT field, press the
menu key to obtain a payment of -315.17 (i.e., PMT
= -$315.17).
soft
To determine the maximum loan possible if the
monthly payments are only $300, type the value
–300 in the PMT field, highlight the PV field, and
press the soft menu key. The resulting value is
PV = $15,705.85.
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12-5
Example 2 - Mortgage with balloon payment
Suppose you have taken out a 30-year, $150,000 house
mortgage at 6.5% annual interest. You expect to sell the
house in 10 years, repaying the loan in a balloon
payment. Find the size of the balloon payment, the value
of the mortgage after 10 years of payment.
Solution. The following cash flow diagram illustrates the
case of the mortgage with balloon payment:
l%YR = 6.5
PV = $150,000
N = 30 x 12 = 360 (for PMT)
N = 10 x 12 = 120 (for balloon payment)
P/YR = 12; End mode
1
2
59
60
PMT = ?
Balloon payment,
FV = ?
•
•
Start the Finance Solver, selecting P/YR = 12 and
End payment option.
Enter the known TVM variables as shown in the
diagram above. Your input form, for calculating
monthly payments for the 30-yr mortgage, should
look as follows:
•
•
Highlighting the PMT field, press the
menu key to obtain a payment of -948.10 (i.e., PMT
= -$948.10)
soft
To determine the balloon payment or future value (FV)
for the mortgage after 10 years, use N = 120,
highlight the FV field, and press the
soft menu
key. The resulting value is FV = -$127,164.19. The
negative value indicates a payment from the
homeowner. Check that the required balloon
payments at the end of 20 years (N=240) and 25
years (N = 300) are -$83,497.92 and
-$48,456.24, respectively.
12-6
Using the Finance Solver
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Calculating Amortizations
Amortization calculations, which also use the TVM
variables, determine the amounts applied towards
principal and interest in a payment or series of payments.
To calculate amortizations:
1. Start the Finance Solver as indicated at the beginning
of this section.
2. Set the following TVM variables:
a
b
Number of payments per year (P/YR)
Payment at beginning or end of periods
3. Store values for the TVM variables I%YR, PV, PMT,
and FV, which define the payment schedule.
4. Press the
soft menu key and enter the
number of payments to amortize in this batch.
5. Press the
soft menu key to amortize a batch of
payments. The calculator will provide for you the
amount applied to interest, to principal, and the
remaining balance after this set of payments have
been amortized.
Example 3 - Amortization for home mortgage
For the data of Example 2 above, find the amortization of
the loan after the first 10 years (12x10 = 120 payments).
Pressing the
screen to the left. Enter 120 in the PAYMENTS field, and
press the soft menu key to produce the results
shown to the right.
soft menu key produces the
To continue amortizing the loan:
1. Press the
soft menu key to store the new
balance after the previous amortization as PV.
2. Enter the number of payments to amortize in the new
batch.
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12-7
3. Press the
soft menu key to amortize the new
batch of payments. Repeat steps 1 through 3 as
often as needed.
Example 4 - Amortization for home mortgage
For the results of Example 3, show the amortization of the
next 10 years of the mortgage loan. First, press the
soft menu key. Then, keeping 120 in the PAYMENTS
field, press the
shown below.
soft menu key to produce the results
To amortize a series of future payments starting at payment p:
1. Calculate the balance of the loan at payment p-1.
2. Store the new balance in PV using the
menu key.
soft
3. Amortize the series of payments starting at the new
PV.
The amortization operation reads the values from the
TVM variables, rounds the numbers it gets from PV and
PMT to the current display mode, then calculates the
amortization rounded to the same setting. The original
variables are not changed, except for PV, which is
updated after each amortization.
12-8
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13
Using mathematical functions
Math functions
The HP 39gs contains many math functions. The functions
are grouped in categories. For example, the Matrix
category contains functions for manipulating matrices.
The Probability category (shown as Prob.on the MATH
menu) contains functions for working with probability.
To use a math function, you enter the function onto the
command line, and include the arguments in parentheses
after the function. You can also select a math function
from the MATH menu.
The MATH menu
The MATH menu provides access to math functions,
physical constants, and programming constants.
The MATH menu is organized by category. For each
category of functions on the left, there is a list of function
names on the right. The highlighted category is the
current category.
•
When you press
, you see the menu list of
Math categories in the left column and the
corresponding functions of the highlighted category
in the right column. The menu key
indicates
that the MATH FUNCTIONS menu list is active.
To select a function
1. Press
to display the MATH menu. The
categories appear in alphabetical order. Press
or
to scroll through the categories. To skip directly to
a category, press the first letter of the category’s
name. Note: You do not need to press
first.
Using mathematical functions
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2. The list of functions (on the right) applies to the
currently highlighted category (on the left). Use
and
to switch between the category list and the
function list.
3. Highlight the name of the function you want and
press
. This copies the function name (and an
initial parenthesis, if appropriate) to the edit line.
Function categories
•
•
Calculus
•
•
•
•
•
Loop
•
•
•
Symbolic
Tests
Complex
numbers
Matrix
Polynomial
Probability
Trigonometry
(Trig)
•
•
•
Constant
Convert
Real numbers
(Real)
Hyperbolic
trigonometry
(Hyperb.)
•
Two-variable
statistics
(Stat-Two)
•
Lists
Math functions by category
Syntax
Each function’s definition includes its syntax, that is, the
exact order and spelling of a function’s name, its
delimiters (punctuation), and its arguments. Note that the
syntax for a function does not require spaces.
Functions common to keyboard and menus
These functions are common to the keyboard and MATH
menu.
For a description, see “π” on
page 13-8.
π
For a description, see “ARG” on
page 13-7.
ARG
For a description, see “ ” on
∂
page 11-7.
For a description, see “AND” on
page 13-19.
AND
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For a description, see
!
“COMB(5,2) returns 10. That is,
there are ten different ways that
five things can be combined two
at a time.!” on page 13-12.
For a description, see “Σ” on
page 13-11.
∑
For a description, see “Scientific
notation (powers of 10)” on
page 1-20.
EEX
∫
∫
For a description, see “ ” on
page 11-7.
The multiplicative inverse
function finds the inverse of a
square matrix, and the
x–1
multiplicative inverse of a real or
complex number. Also works on
a list containing only these object
types.
Keyboard functions
The most frequently used functions are available directly
from the keyboard. Many of the keyboard functions also
accept complex numbers as arguments.
,
,
,
Add, Subtract, Multiply, Divide. Also accepts complex
numbers, lists and matrices.
value1+ value2, etc.
x
e
Natural exponential. Also accepts complex numbers.
e^value
Example
e^5returns 148.413159103
Natural logarithm. Also accepts complex numbers.
LN(value)
Example
LN(1)returns 0
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13-3
x
10
Exponential (antilogarithm). Also accepts complex
numbers.
10^value
Example
10^3 returns 1000
Common logarithm. Also accepts complex numbers.
LOG(value)
Example
LOG(100) returns 2
,
,
Sine, cosine, tangent. Inputs and outputs depend on the
current angle format (Degrees, Radians, or Grads).
SIN(value)
COS(value)
TAN(value)
Example
TAN(45) returns 1 (Degrees mode).
–1
ASIN
Arc sine: sin x. Output range is from –90° to 90°, –π/2
to π/2, or –100 to 100 grads. Inputs and outputs depend
on the current angle format. Also accepts complex
numbers.
ASIN(value)
Example
ASIN(1) returns 90 (Degrees mode).
–1
ACOS
Arc cosine: cos x. Output range is from 0° to 180°, 0 to
π, or 0 to 200 grads. Inputs and outputs depend on the
current angle format. Also accepts complex numbers.
Output will be complex for values outside the normal
COS domain of –1 ≤ x ≤ 1 .
ACOS(value)
Example
ACOS(1)returns 0(Degrees mode).
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–1
ATAN
Arc tangent: tan x. Output range is from –90° to 90°,
2π/2 to π/2, or –100 to 100 grads. Inputs and outputs
depend on the current angle format. Also accepts
complex numbers.
ATAN(value)
Example
ATAN(1)returns 45(Degrees mode).
Square. Also accepts complex numbers.
2
value
Example
2
18 returns 324
Square root. Also accepts complex numbers.
value
Example
324 returns 18
Negation. Also accepts complex numbers.
–value
Example
-(1,2) returns (-1,-2)
Power (x raised to y). Also accepts complex numbers.
value^power
Example
2^8 returns 256
ABS
Absolute value. For a complex number, this is x2 + y2 .
ABS(value)
ABS((x,y))
Example
ABS(–1) returns 1
ABS((1,2))returns 2.2360679775
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n
Takes the nth root of x.
root NTHROOT value
Example
Calculus functions
The symbols for differentiation and integration are
available directly form the keyboard—
respectively—as well as from the MATH menu.
and S
Differentiates expression with respect to the variable of
differentiation. From the command line, use a formal
name (S1, etc.) for a non-numeric result. See “Finding
derivatives” on page 13-21.
∂
variable(expression)
∂
Example
s1(s1 +3*s1)returns 2*s1+3
2
∂
∫
Integrates expression from lower to upper limits with
respect to the variable of integration. To find the definite
integral, both limits must have numeric values (that is, be
numbers or real variables). To find the indefinite integral,
one of the limits must be a formal variable (s1, etc).
∫
(lower, upper, expression, variable)
See “Using formal variables” on page 13-20 for
further details.
Example
∫
(0,s1,2*X+3,X)
finds the indefinite result 3*s1+2*(s1^2/2)
See “To find the indefinite integral using formal
variables” on page 13-23 for more information on
finding indefinite integrals.
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TAYLOR
Calculates the nth order Taylor polynomial of expression
at the point where the given variable = 0.
TAYLOR(expression, variable, n)
Example
2
TAYLOR(1 + sin(s1) ,s1,5)with Radians
angle measure and Fraction number format (set in
MODES) returns 1+s1^2-1/3*s1^4.
Complex number functions
These functions are for complex numbers only. You can
also use complex numbers with all trigonometric and
hyperbolic functions, and with some real-number and
keyboard functions. Enter complex numbers in the form
(x,y), where x is the real part and y is the imaginary part.
ARG
Argument. Finds the angle defined by a complex number.
Inputs and outputs use the current angle format set in
Modes.
ARG((x, y))
Example
ARG((3,3)) returns 45 (Degrees mode)
CONJ
Complex conjugate. Conjugation is the negation (sign
reversal) of the imaginary part of a complex number.
CONJ((x, y))
Example
CONJ((3,4)) returns (3,-4)
IM
RE
Imaginary part, y, of a complex number, (x, y).
IM ((x, y))
Example
IM((3,4)) returns 4
Real part x, of a complex number, (x, y).
RE((x, y))
Example
RE((3,4)) returns 3
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Constants
The constants available from the MATH FUNCTIONS
menu are mathematical constants. These are described in
this section. The hp 39gs has two other menus of
constants: program constants and physical constants.
These are described in “Program constants and physical
constants” on page 13-24.
e
Natural logarithm base. Internally represented as
2.71828182846.
e
i
Imaginary value for –1 , the complex number (0,1).
i
MAXREAL
Maximum real number. Internally represented as
499
9.99999999999 x10
.
MAXREAL
MINREAL
Minimum real number. Internally represented as
-499
1x10
.
MINREAL
π
Internally represented as 3.14159265359.
π
Conversions
The conversion functions are found on the Convert
menu. They enable you to make the following
conversions.
→C
→F
Convert from Fahrenheit to Celcius.
Example
→C(212) returns 100
Convert from Celcius to Fahrenheit.
Example
→F(0) returns 32
→CM
Convert from inches to centimeters.
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→IN
Convert from centimeters to inches.
Convert from US gallons to liters.
Convert from liters to US gallons.
Convert from pounds to kilograms.
Convert from kilograms to pounds.
Convert from miles to kilometers.
Convert from kilometers to miles.
Convert from radians to degrees.
Convert from degrees to radians.
→L
→LGAL
→KG
→LBS
→KM
→MILE
→DEG
→RAD
Hyperbolic trigonometry
The hyperbolic trigonometry functions can also take
complex numbers as arguments.
–1
ACOSH
ASINH
ATANH
COSH
SINH
Inverse hyperbolic cosine : cosh x.
ACOSH(value)
–1
Inverse hyperbolic sine : sinh x.
ASINH(value)
–1
Inverse hyperbolic tangent : tanh x.
ATANH(value)
Hyperbolic cosine
COSH(value)
Hyperbolic sine.
SINH(value)
TANH
ALOG
Hyperbolic tangent.
TANH(value)
Antilogarithm (exponential). This is more accurate than
10^xdue to limitations of the power function.
ALOG(value)
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EXP
Natural exponential. This is more accurate than ex due
to limitations of the power function.
EXP(value)
EXPM1
LNP1
Exponent minus 1 : ex – 1 . This is more accurate than
EXPM1(value)
Natural log plus 1 : ln(x+1). This is more accurate than
the natural logarithm function when xis close to zero.
LNP1(value)
List functions
These functions work on list data. See “List functions” on
page 16-6.
Loop functions
The loop functions display a result after evaluating an
expression a given number of times.
ITERATE
Repeatedly for #times evaluates an expression in terms of
variable. The value for variable is updated each time,
starting with initialvalue.
ITERATE(expression, variable, initialvalue,
#times)
Example
2
ITERATE(X ,X,2,3) returns 256
RECURSE
Provides a method of defining a sequence without using
the Symbolic view of the Sequence aplet. If used with |
(“where”), RECURSE will step through the evaluation.
RECURSE(sequencename, term , term , term )
n
1
2
Example
RECURSE(U,U(N-1)*N,1,2)
U1(N)
Stores a factorial-calculating function named U1.
When you enter U1(5), for example, the function
calculates 5! (120).
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Σ
Σ(variable=initialvalue, finalvalue, expression)
Example
2
Σ(C=1,5,C )returns 55.
Matrix functions
These functions are for matrix data stored in matrix
variables. See “Matrix functions and commands” on
page 15-10.
Polynomial functions
Polynomials are products of constants (coefficients) and
variables raised to powers (terms).
POLYCOEF
POLYEVAL
POLYFORM
Polynomial coefficients. Returns the coefficients of the
polynomial with the specified roots.
POLYCOEF([roots])
Example
To find the polynomial with roots 2, –3, 4, –5:
POLYCOEF([2,-3,4,-5]) returns[1,2,-25,
4
3
2
-26,120], representing x +2x –25x –26x+120.
Polynomial evaluation. Evaluates a polynomial with the
specified coefficients for the value of x.
POLYEVAL([coefficients], value)
Example
4
3
2
For x +2x –25x –26x+120:
POLYEVAL([1,2,-25,-26,120],8)returns
3432.
Polynomial form. Creates a polynomial in variable1 from
expression.
POLYFORM(expression, variable1)
Example
POLYFORM((X+1)^2+1,X)returns X^2+2*X+2.
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POLYROOT
Polynomial roots. Returns the roots for the nth-order
polynomial with the specified n+1 coefficients.
POLYROOT([coefficients])
Example
4
3
2
For x +2x –25x –26x+120:
POLYROOT([1,2,-25,-26,120])returns
[2,-3,4,-5].
H I N T
The results of POLYROOT will often not be easily seen in
HOME due to the number of decimal places, especially if
they are complex numbers. It is better to store the results
of POLYROOT to a matrix.
For example, POLYROOT([1,0,0,-8]
M1will
store the three complex cube roots of 8 to matrix M1 as
a complex vector. Then you can see them easily by going
to the Matrix Catalog. and access them individually in
calculations by referring to M1(1), M1(2) etc.
Probability functions
COMB
Number of combinations (without regard to order) of n
things taken r at a time: n!/(r!(n-r)).
COMB(n, r)
Example
COMB(5,2) returns 10. That is, there are ten
different ways that five things can be combined two
at a time.!
Factorial of a positive integer. For non-integers, ! = Γ(x +
1). This calculates the gamma function.
value!
PERM
Number of permutations (with regard to order) of n things
taken r at a time: n!/(r!(n-r)!
PERM(n, r)
Example
PERM(5,2) returns 20. That is, there are 20
different permutations of five things taken two at a
time.
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RANDOM
Random number (between zero and 1). Produced by a
pseudo-random number sequence. The algorithm used in
the RANDOM function uses a seed number to begin its
sequence. To ensure that two calculators must produce
different results for the RANDOM function, use the
RANDSEED function to seed different starting values
before using RANDOM to produce the numbers.
RANDOM
H I N T
The setting of Time will be different for each calculator, so
using RANDSEED(Time) is guaranteed to produce a set of
numbers which are as close to random as possible. You
can set the seed using the command RANDSEED.
UTPC
UTPF
Upper-Tail Chi-Squared Probability given degrees of
freedom, evaluated at value. Returns the probability that
2
a χ random variable is greater than value.
UTPC(degrees, value)
Upper-Tail Snedecor’s F Probability given numerator
degrees of freedom and denominator degrees of freedom
(of the F distribution), evaluated at value. Returns the
probability that a Snedecor's F random variable is
greater than value.
UTPF(numerator, denominator, value)
UTPN
UTPT
Upper-Tail Normal Probability given mean and variance,
evaluated at value. Returns the probability that a normal
random variable is greater than value for a normal
distribution. Note: The variance is the square of the
standard deviation.
UTPN(mean, variance, value)
Upper-Tail Student’s t-Probability given degrees of
freedom, evaluated at value. Returns the probability that
the Student's t- random variable is greater than value.
UTPT(degrees, value)
Real-number functions
Some real-number functions can also take complex
arguments.
CEILING
Smallest integer greater than or equal to value.
CEILING(value)
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Examples
CEILING(3.2) returns 4
CEILING(-3.2) returns -3
DEG→RAD
Degrees to radians. Converts value from Degrees angle
format to Radians angle format.
DEG→RAD(value)
Example
DEG→RAD(180) returns 3.14159265359, the
value of π.
FLOOR
Greatest integer less than or equal to value.
FLOOR(value)
Example
FLOOR(-3.2) returns -4
FNROOT
Function root-finder (like the Solve aplet). Finds the value
for the given variable at which expression most nearly
evaluates to zero. Uses guess as initial estimate.
FNROOT(expression, variable, guess)
Example
FNROOT(M*9.8/600-1,M,1) returns
61.2244897959.
FRAC
Fractional part.
FRAC(value)
Example
FRAC(23.2) returns .2
HMS→
Hours-minutes-seconds to decimal. Converts a number or
expression in H.MMSSs format (time or angle that can
include fractions of a second) to x.x format (number of
hours or degrees with a decimal fraction).
HMS→(H.MMSSs)
Example
HMS→(8.30) returns 8.5
→HMS
Decimal to hours-minutes-seconds. Converts a number or
expression in x.xformat (number of hours or degrees
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with a decimal fraction) to H.MMSSs format (time or
angle up to fractions of a second).
→HMS(x.x)
Example
→HMS(8.5) returns 8.3
INT
Integer part.
INT(value)
Example
INT(23.2) returns 23
MANT
MAX
Mantissa (significant digits) of value.
MANT(value)
Example
MANT(21.2E34) returns 2.12
Maximum. The greater of two values.
MAX(value1, value2)
Example
MAX(210,25) returns 210
MIN
MOD
%
Minimum. The lesser of two values.
MIN(value1, value2)
Example
MIN(210,25)returns 25
Modulo. The remainder of value1/value2.
value1 MODvalue2
Example
9MOD 4 returns 1
xpercent of y; that is, x/100*y.
%(x, y)
Example
%(20,50) returns 10
%CHANGE
Percent change from x to y, that is, 100(y–x)/x.
%CHANGE(x, y)
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Example
%CHANGE(20,50) returns 150
%TOTAL
Percent total : (100)y/x. What percentage of x, is y.
%TOTAL(x, y)
Example
%TOTAL(20,50) returns 250
RAD→DEG
Radians to degrees. Converts value from radians to
degrees.
RAD→DEG(value)
Example
RAD→DEG(π) returns 180
ROUND
Rounds value to decimal places. Accepts complex
numbers.
ROUND(value, places)
Round can also round to a number of significant digits as
showed in example 2.
Examples
ROUND(7.8676,2) returns 7.87
ROUND (0.0036757,-3) returns 0.00368
SIGN
Sign of value. If positive, the result is 1. If negative, –1. If
zero, result is zero. For a complex number, this is the unit
vector in the direction of the number.
SIGN(value)
SIGN((x, y))
Examples
SIGN (–2)returns –1
SIGN((3,4)) returns (.6,.8)
TRUNCATE
Truncates value to decimal places. Accepts complex
numbers.
TRUNCATE(value, places)
Example
TRUNCATE(2.3678,2) returns 2.36
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XPON
Exponent of value.
XPON(value)
Example
XPON(123.4) returns 2
Two-variable statistics
These are functions for use with two-variable statistics.
See “Two-variable” on page 10-15.
Symbolic functions
The symbolic functions are used for symbolic
manipulations of expressions. The variables can be
formal or numeric, but the result is usually in symbolic
form (not a number). You will find the symbols for the
symbolic functions = and | (where) in the CHARS menu
(
CHARS) as well as the MATH menu.
= (equals)
ISOLATE
Sets an equality for an equation. This is not a logical
operator and does not store values. (See “Test functions”
on page 13-18.)
expression1=expression2
Isolates the first occurrence of variable in expression=0
and returns a new expression, where
variable=newexpression. The result is a general solution
that represents multiple solutions by including the (formal)
variables S1 to represent any sign and n1 to represent
any integer.
ISOLATE(expression, variable)
Examples
ISOLATE(2*X+8,X) returns -4
ISOLATE(A+B*X/C,X) returns -(A*C/B)
LINEAR?
Tests whether expression is linear for the specified
variable. Returns 0(false) or 1(true).
LINEAR?(expression, variable)
Example
LINEAR?((X^2-1)/(X+1),X) returns 0
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QUAD
Solves quadratic expression=0 for variable and returns
a new expression, where variable=newexpression. The
result is a general solution that represents both positive
and negative solutions by including the formal variable
S1 to represent any sign: + or – .
QUAD(expression, variable)
Example
2
QUAD((X-1) -7,X) returns
(2+s1*5.29150262213)/2
QUOTE
Encloses an expression that should not be evaluated
numerically.
QUOTE(expression)
Examples
QUOTE(SIN(45))
expression SIN(45) rather than the value of SIN(45).
F1(X) stores the
Another method is to enclose the expression in single
quotes.
For example, X^3+2*X
F1(X)puts the
expression X^3+2*X into F1(X)in the Function
aplet.
| (where)
Evaluates expression where each given variable is set to
the given value. Defines numeric evaluation of a symbolic
expression.
expression|(variable1=value1, variable2=value2,...)
Example
3*(X+1)|(X=3) returns 12.
Test functions
The test functions are logical operators that always return
either a 1 (true) or a 0 (false).
<
≤
Less than. Returns 1 if true, 0 if false.
value1<value2
Less than or equal to. Returns 1 if true, 0 if false.
value1≤value2
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= =
Equals (logical test). Returns 1 if true, 0 if false.
value1==value2
≠
>
Not equal to. Returns 1 if true, 0 if false.
value1≠value2
Greater than. Returns 1 if true, 0 if false.
value1>value2
≥
Greater than or equal to. Returns 1 if true, 0 if false.
value1≥value2
AND
Compares value1 and value2. Returns 1 if they are both
non-zero, otherwise returns 0.
value1 AND value2
IFTE
If expression is true, do the trueclause; if not, do the
falseclause.
IFTE(expression, trueclause, falseclause)
Example
2 3
IFTE(X>0,X ,X )
NOT
OR
Returns 1 if value is zero, otherwise returns 0.
NOT value
Returns 1 if either value1 or value2 is non-zero, otherwise
returns 0.
value1 OR value2
XOR
Exclusive OR. Returns 1 if either value1 or value2—but
not both of them—is non-zero, otherwise returns 0.
value1 XOR value2
Trigonometry functions
The trigonometry functions can also take complex
numbers as arguments. For SIN, COS, TAN, ASIN,
ACOS, and ATAN, see the Keyboard category.
ACOT
Arc cotangent.
ACOT(value)
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ACSC
ASEC
COT
CSC
Arc cosecant.
ACSC(value)
Arc secant.
ASEC(value)
Cotangent: cosx/sinx.
COT(value)
Cosecant: 1/sinx
CSC(value)
SEC
Secant: 1/cosx.
SEC(value)
Symbolic calculations
The HP 39gs has the ability to perform symbolic
calculations, for example, symbolic integration and
differentiation. You can perform symbolic calculations in
HOME and in the Function aplet.
In HOME
When you perform calculations that contain normal
variables, the calculator substitutes values for any
variables. For example, if you enter A+B on the command
line and press
, the calculator retrieves the values
for A and B from memory and substitutes them in the
calculation.
Using formal
variables
To perform symbolic calculations, for example symbolic
differentiations and integrations, you need to use formal
names. The HP 39gs has six formal names available for
use in symbolic calculations. These are S0 to S5. When
you perform a calculation that contains a formal name,
the HP 39gs does not carry out any substitutions.
You can mix formal names and real variables. Evaluating
2
(A+B+S1) will evaluate A+B, but not S1.
If you need to evaluate an expression that contains formal
names numerically, you use the | (where) command,
listed in the Math menu under the Symbolic category.
2
For example to evaluate (S1*S2) when S1=2 and
S2=4, you would enter the calculation as follows:
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(The | symbol is in the CHARS menu: press
CHARS.
The = sign is listed in the MATH menu under Symbolic
functions.)
Symbolic
You can perform symbolic operations in the Function
aplet’s Symbolic view. For example, to find the derivative
of a function in the Function aplet’s Symbolic view, you
define two functions and define the second function as a
derivative of the first function. You then evaluate the
second function. See “To find derivatives in the Function
aplet’s Symbolic view” on page 13-22 for an example.
calculations in
the Function
aplet
Finding derivatives
The HP 39gs can perform symbolic differentiation on
some functions. There are two ways of using the HP 39gs
to find derivatives.
•
You can perform differentiations in HOME by using
the formal variables, S1 to S5.
•
You can perform differentiations of functions of X in
the Function aplet.
To find derivatives
in HOME
To find the derivative of the function in HOME, use a
formal variable in place of X. If you use X, the
differentiation function substitutes the value that X holds,
and returns a numeric result.
For example, consider the function:
dx(sin(x2 ) + 2cos(x))
1. Enter the differentiation function onto the command
line, substituting S1 in place of X.
S1
S1
2
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S1
2. Evaluate the function.
3. Show the result.
To find derivatives
in the Function
aplet’s Symbolic
view
To find the derivative of the function in the Function aplet’s
Symbolic view, you define two functions and define the
second function as a derivative of the first function. For
example, to differentiate sin(x2) + 2cosx :
1. Access the Function aplet’s Symbolic view and define
F1.
2
2. Define F2(X) as the
derivative of F(1).
F1
3. Select F2(X) and
evaluate it.
13-22
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4. Press
to display
the result. Note: Use
the arrow keys to view
the entire function.
|
You could also just define
F1(x)= dx(sin(x2) + 2cos(x)) .
To find the
For example, to find the indefinite integral of
3x2 – 5dx use:
indefinite integral
using formal
variables
∫
∫
2
0, S1, 3 X − 5, X
)
1. Enter the function.
0
S1
X
3
5
X
2. Show the result format.
3. Press
to close the
show window.
4. Copy the result and
evaluate.
Thus, substituting X for S1, it can be seen that:
x3
⎛
⎜
⎜
⎜
⎝
⎞
⎟
⎟
⎟
⎠
----
3
3x2 – 5dx= – 5x + 3
---------------
∫
∂
(X)
∂X
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This result is derived from substituting X=S1 and X=0 into
the original expression found in step 1. However,
substituting X=0 will not always evaluate to zero and may
result in an unwanted constant.
(x – 2)5
To see this, consider: (x – 2)4dx=
-------------------
∫
5
The ‘extra’ constant of 6.4
results from the
substitution of x = 0 into
5
(x – 2) /5, and should be
disregarded if an
indefinite integral is
required.
Program constants and physical constants
When you press
, three menus of functions and
constants become available:
•
•
•
the math functions menu (which appears by default)
the program constants menu, and
the physical constants menu.
The math functions menu is described extensively earlier
in this chapter.
Program constants
The program constants are numbers that have been
assigned to various calculator settings to enable you to
test for or specify such a setting in a program. For
example, the various display formats are assigned the
following numbers:
1 Standard
2 Fixed
3 Scientific
4 Engineering
5 Fraction
6 Mixed fraction
In a program, you could store the constant number of a
particular format into a variable and then subsequently
test for that particular format.
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To access the menu of program constants:
1. Press
2. Press
.
.
3. Use the arrow keys to navigate through the options.
assigned to the option you selected in the previous
step.
The use of program constants is illustrated in more detail
in “Programming” on page 18-1
Physical constants
There are 29 physical constants—from the fields of
chemistry, physics and quantum mechanics—that you
can use in calculations. A list of all these constants can be
found in “Physical Constants” on page R-16.
To access the menu of physical constants:
1. Press
2. Press
.
.
3. Use the arrow keys to navigate through the options.
4. To see the symbol and value of a selected constant,
press
. (Click
to close the information
window that appears.)
The following example shows the information
available about the speed of light (one of the physics
constants).
5. To use the selected constant in a calculation, press
. The constant appears at the position of the
cursor on the edit line.
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13-25
Example
Suppose you want to know the potential energy of a mass
of 5 units according to the equation E = mc2 .
1. Enter 5
2. Press
and then press
.
3. Select light s...from the Physics menu.
4. Press
. The menu closes and the value of the
selected constant is copied to the edit line.
5. Complete the equation as you would normally and
press
to get the result.
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14
Variables and memory management
Introduction
The HP 39gs has approximately 200K of user memory.
The calculator uses this memory to store variables,
perform computations, and store history.
A variable is an object that you create in memory to hold
data. The hp 39gs has two types of variables, home
variables and aplet variables.
•
Home variables are available in all aplets. For
example, you can store real numbers in variables A
to Z and complex numbers in variables Z0 to Z9.
These can be numbers you have entered, or the
results of calculations. These variables are available
within all aplets and within any programs.
•
Aplet variables apply only to a single aplet. Aplets
have specific variables allocated to them which vary
from aplet to aplet.
You use the calculator’s memory to store the following
objects:
•
•
•
•
•
copies of aplets with specific configurations
new aplets that you download
aplet variables
home variables
variables created through a catalog or editor, for
example a matrix or a text note
•
programs that you create.
You can use the Memory Manager (
MEMORY) to
view the amount of memory available. The catalog views,
which are accessible via the Memory Manager, can be
used to transfer variables such as lists or matrices
between calculators.
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14-1
Storing and recalling variables
You can store numbers or expressions from a previous
input or result into variables.
Numeric Precision
A number stored in a variable is always stored as a 12-
digit mantissa with a 3-digit exponent. Numeric precision
in the display, however, depends on the display mode
(Standard, Fixed, Scientific, Engineering, or Fraction). A
displayed number has only the precision that is
displayed. If you copy it from the HOME view display
history, you obtain only the precision displayed, not the
full internal precision. On the other hand, the variable
Ans always contains the most recent result to full
precision.
To store a value
1. On the command line,
enter the value or the
calculation for the result
you wish to store.
2. Press
3. Enter a name for the
variable.
4. Press
.
To store the results
of a calculation
If the value you want to store is in the HOME view display
history, for example the results of a previous calculation,
you need to copy it to the command line, then store it.
1. Perform the calculation for the result you want to store.
3
3
8
6
2. Move the highlight to the result you wish to store.
3. Press
4. Press
to copy the result to the command line.
.
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5. Enter a name for the variable.
A
6. Press
to store the result.
The results of a calculation can also be stored directly to
a variable. For example:
2
5
3
B
To recall a value
To recall a variable’s value, type the name of the variable
and press
.
A
To use variables in
calculations
You can use variables in calculations. The calculator
substitutes the variable’s value in the calculation:
65
A
To clear a variable
You can use the CLRVAR
command to clear a
specified variable. For
example, if you have
stored{1,2,3,4}invariable
L1, entering CLRVAR L1
will clear L1. (You can find the CLRVAR command
by pressing
category of commands.)
and choosing the PROMPT
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14-3
The VARS menu
You use the VARS menu to access all variables in the
calculator. The VARS menu is organised by category. For
each variable category in the left column, there is a list of
variables in the right column. You select a variable
category and then select a variable in the category.
1. Open the VARS menu.
2. Use the arrow keys or press the alpha key of the first
letter in the category to select a variable category.
For example, to select
the Matrix category,
press
.
Note: In this instance,
there is no need to
press the ALPHA key.
3. Move the highlight to the variables column.
4. Use the arrow keys to select the variable that you
want. For example, to select M2, press
.
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5. Choose whether to place the variable name or the
variable value on the command line.
–
Press
to indicate that you want the
variable’s contents to appear on the command
line.
–
Press
to indicate that you want the
variable’s name to appear on the command line.
6. Press to place the value or name on the
command line. The selected object appears on the
command line.
Note: The VARS menu can also be used to enter the
names or values of variables into programs.
Example
This example demonstrates how to use the VARS menu to
add the contents of two list variables, and to store the
result in another list variable.
1. Display the List Catalog.
LIST
to select L1
2. Enter the data for L1.
88
65
90
70
89
3. Return to the List Catalog to create L2.
LIST
to select L2
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14-5
4. Enter data for L2.
55
90
48
77
86
5. Press
to access HOME.
6. Open the variable menu and select L1.
7. Copy it to the command line. Note: Because the
option is highlighted, the variable’s name,
rather than its contents, is copied to the command
line.
8. Insert the + operator and select the L2 variable from
the List variables.
9. Store the answer in the List catalog L3 variable.
L3
Note: You can also
type list names directly
from the keyboard.
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Home variables
It is not possible to store data of one type in a variable of
another type. For example, you use the Matrix catalog to
create matrices. You can create up to ten matrices, and
you can store these in variables M0 to M9. You cannot
store matrices in variables other than M0 to M9.
Cate-
gory
Available names
Complex Z0 to Z9
For example, (1,2)
Z1. You can enter a complex
number by typing (r,i), where r represents
the real part, and i represents the
imaginary part.
Graphic
Library
G0 to G9
See“Graphic commands” on page 18-21
for more information on storing graphic
objects via programming commands. See
“To store into a graphics variable” on
page 17-5 for more information on
storing graphic object via the sketch view.
Aplet library variables can store aplets
that you have created, either by saving a
copy of a standard aplet, or downloading
an aplet from another source.
List
L0 to L9
For example, {1,2,3}
M0 to M9 can store matrices or vectors.
For example, [[1,2],[3,4]] M0.
L1.
Matrix
Modes
Modes variables store the modes settings
that you can configure using
MODES.
Notepad Notepad variables store notes.
Program
Real
Program variables store programs.
A to Z and θ.
For example, 7.45
A.
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14-7
Aplet variables
Most aplet variables store values that are unique to a
particular aplet. These include symbolic expressions and
equations (see below), settings for the Plot and Numeric
views, and the results of some calculations such as roots
and intersections.
See the Reference Information chapter for more
information about aplet variables.
Category Available names
Function
F0 to F9 (Symbolic view). See “Function
aplet variables” on page R-7.
Parametric
X0, Y0 to X9, Y9 (Symbolic view). See
“Parametric aplet variables” on page
R-8.
Polar
R0 to R9 (Symbolic view). See “Polar
aplet variables” on page R-9.
Sequence
U0 to U9 (Symbolic view). See
“Sequence aplet variables” on page
R-10.
Solve
E0 to E9 (Symbolic view). See “Solve
aplet variables” on page R-11.
Statistics
C0 to C9 (Numeric view). See
“Statistics aplet variables” on page
R-12.
To access an aplet
variable
1. Open the aplet that contains the variable you want to
recall.
2. Press
to display the VARS menu.
3. Use the arrow keys to select a variable category in
the left column, then press
in the right column.
to access the variables
4. Use the arrow keys to select a variable in the right
column.
5. To copy the name of the variable onto the edit line,
press
. (
is the default setting.)
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6. To copy the value of the
variable into the edit
line, press
press
and
.
Memory Manager
You can use the Memory Manager to determine the
amount of available memory on the calculator. You can
also use Memory Manager to organize memory. For
example, if the available memory is low, you can use the
Memory Manager to determine which aplets or variables
consume large amounts of memory. You can make
deletions to free up memory.
Example
1. Start the Memory Manager. A list of variable
categories is displayed.
MEMORY
Free memory is
displayed in the top
right corner and the
body of the screen lists
each category, the memory it uses, and the
percentage of the total memory it uses.
2. Select the category with which you want to work and
press
. Memory Manager displays memory
details of variables within the category.
3. To delete variables in a category:
–
–
Press
Press
to delete the selected variable.
CLEAR to delete all variables in the
selected category.
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15
Matrices
Introduction
You can perform matrix calculations in HOME and in
programs. The matrix and each row of a matrix appear
in brackets, and the elements and rows are separated by
commas. For example, the following matrix:
1 2 3
4 5 6
is displayed in the history as:
[[1,2,3],[4,5,6]]
(If the Decimal Mark mode is set to Comma, then separate
each element and each row with a period.)
You can enter matrices directly in the command line, or
create them in the matrix editor.
Vectors
Vectors are one-dimensional arrays. They are composed
of just one row. A vector is represented with single
brackets; for example, [1,2,3]. A vector can be a real
number vector or a complex number vector, for example
[(1,2), (7,3)].
Matrices
Matrices are two-dimensional arrays. They are composed
of more than one row and more than one column.
Two-dimensional matrices are represented with nested
brackets; for example, [[1,2,3],[4,5,6]]. You can create
complex matrices, for example, [[(1,2), (3,4)], [(4,5),
(6,7)]].
Matrix Variables
There are ten matrix variables available, named M0 to
M9. You can use them in calculations in HOME or in a
program. You can retrieve the matrix names from the
VARS menu, or just type their names from the keyboard.
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Creating and storing matrices
You can create, edit,
delete, send, and receive
matrices in the Matrix
catalog.
To open the Matrix
catalog, press
MATRIX.
You can also create and store matrices—named or
unnamed—-in HOME. For example, the command:
POLYROOT([1,0,–1,0])ꢂM1
stores the root of the complex vector of length 3 into the
M1 variable. M1 now contains the three roots of
x3 – x = 0
Matrix Catalog
keys
The table below lists the operations of the menu keys in
the Matrix Catalog, as well as the use of Delete (
)
and Clear (
CLEAR).
Key
Meaning
Opens the highlighted matrix for
editing.
Prompts for a matrix type, then
highlighted name.
Transmits the highlighted matrix to
another hp 39gs or a disk drive.
See “Sending and receiving aplets”
on page 19-4.
Receives a matrix from another
hp 39gs or a disk drive. See
“Sending and receiving aplets” on
page 19-4.
Clears the highlighted matrix.
Clears all matrices.
CLEAR
or
Moves to the end or the beginning
of the catalog.
15-2
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To create a matrix
in the Matrix
Catalog
1. Press
MATRIX to open the Matrix Catalog. The
Matrix catalog lists the 10 available matrix variables,
M0 to M9.
2. Highlight the matrix variable name you want to use
and press
.
3. Select the type of matrix to create.
– For a vector (one-dimensional array),
select Realvectoror Complex vector.
Certain operations (+, –, CROSS) do not
recognize a one-dimensional matrix as a vector,
so this selection is important.
– For a matrix (two-dimensional array),
select Realmatrix or Complexmatrix.
4. For each element in the matrix, type a number or an
expression, and press
. (The expression may
not contain symbolic variable names.)
For complex numbers, enter each number in
complex form; that is, (a, b), where a is the real part
and b is the imaginary part. You must include the
parentheses and the comma.
5. Use the cursor keys to move to a different row or
column. You can change the direction of the highlight
bar by pressing
. The
menu key toggles
between the following three options:
–
–
specifies that the cursor moves to the cell
below the current cell when you press
.
specifies that the cursor moves to the cell to
the right of the current cell when you press
.
–
specifies that the cursor stays in the current
cell when you press
.
6. When done, press
catalog, or press
MATRIX to see the Matrix
to return to HOME. The
matrix entries are automatically stored.
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A matrix is listed with two dimensions, even if it is 3×1. A
vector is listed with the number of elements, such as 3.
To transmit a
matrix
You can send matrices between calculators just as you
can send aplets, programs, lists, and notes.
connect the calculators using an appropriate cable).
2. Open the Matrix catalogs on both calculators.
3. Highlight the matrix to send.
4. Press
and choose the method of sending
(infrared or cable).
5. Press
on the receiving calculator and choose
the method of receiving (infrared or cable).
For more information on sending and receiving files, see
“Sending and receiving aplets” on page 19-4.
Working with matrices
To edit a matrix
In the Matrix catalog, highlight the name of the matrix
you want to edit and press
.
Matrix edit keys
The following table lists the matrix edit key operations.
Key
Meaning
Copies the highlighted element to
the edit line.
Inserts a row of zeros above, or a
column of zeros to the left, of the
highlighted cell. (You are prompted
to choose row or column.)
A three-way toggle for cursor
advancement in the Matrix editor.
advances to the right,
advances downward, and
does not advance at all.
¸
Switches between larger and
smaller font sizes.
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Key
Meaning (Continued)
Deletes the highlighted cells, row,
or column (you are prompted to
make a choice).
CLEAR
Clears all elements from the matrix.
Moves to the first row, last row, first
column, or last column respectively.
To display a matrix
•
•
In the Matrix catalog (
matrix name and press
MATRIX), highlight the
.
In HOME, enter the name of the matrix variable and
press
.
To display one
element
In HOME, enter matrixname(row,column). For example,
if M2is [[3,4],[5,6]], then M2(1,2)
4.
returns
To create a matrix
in HOME
1. Enter the matrix in the edit line. Start and end the
matrix and each row with square brackets (the shifted
and
keys).
2. Separate each element and each row with a comma.
Example: [[1,2],[3,4]].
3. Press
to enter and display the matrix.
The left screen below shows the matrix
[[2.5,729],[16,2]]being stored into M5. The
screen on the right shows the vector [66,33,11]being
stored into M6. Note that you can enter an expression
(like 5/2) for an element of the matrix, and it will be
evaluated.
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To store one
element
In HOME, enter, value
matrixname(row,column).
For example, to change the element in the first row and
second column of M5 to 728, then display the resulting
matrix:
728
M5
1
2
M5
.
An attempt to store an element to a row or column beyond
the size of the matrix results in an error message.
Matrix arithmetic
You can use the arithmetic functions (+, –, ×, / and
powers) with matrix arguments. Division left-multiplies by
the inverse of the divisor. You can enter the matrices
themselves or enter the names of stored matrix variables.
The matrices can be real or complex.
For the next examples, store [[1,2],[3,4]] into M1 and
[[5,6],[7,8]] into M2.
Example
1. Create the first matrix.
MATRIX
1
2
3
4
2. Create the second
matrix.
MATRIX
5
6
7
8
15-6
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3. Add the matrices that
you created.
M1
M2
To multiply and
divide by a scalar
For division by a scalar, enter the matrix first, then the
operator, then the scalar. For multiplication, the order of
the operands does not matter.
The matrix and the scalar can be real or complex. For
example, to divide the result of the previous example by
2, press the following keys:
2
To multiply two
matrices
To multiply the two matrices M1 and M2 that you created
for the previous example, press the following keys:
M1
M
2
To multiply a matrix by a
vector, enter the matrix
first, then the vector. The
number of elements in the vector must equal the number
of columns in the matrix.
To raise a matrix to
a power
You can raise a matrix to any power as long as the power
is an integer. The following example shows the result of
raising matrix M1, created earlier, to the power of 5.
M1
5
Note: You can also raise a
matrix to a power without
first storing it as a variable.
Matrices can be raised to negative powers. In this case,
the result is equivalent to 1/[matrix]^ABS(power). In the
following example, M1 is raised to the power of –2.
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M1
2
To divide by a
square matrix
For division of a matrix or a vector by a square matrix,
the number of rows of the dividend (or the number of
elements, if it is a vector) must equal the number of rows
in the divisor.
This operation is not a mathematical division: it is a left-
multiplication by the inverse of the divisor. M1/M2 is
–1
equivalent to M2 * M1.
To divide the two matrices M1 and M2 that you created
for the previous example, press the following keys:
M1
M2
To invert a matrix
You can invert a square matrix in HOME by typing the
–1
matrix (or its variable name) and pressing
x
. Or you can use the matrix INVERSE command.
Enter INVERSE(matrixname) in HOME and press
.
To negate each
element
You can change the sign of each element in a matrix by
pressing
before the matrix name.
Solving systems of linear equations
Example
Solve the following linear system:
2x + 3y + 4z = 5
x + y – z = 7
4x – y + 2z = 1
1. Open the Matrix
catalog and create a
vector.
MATRIX
15-8
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2. Create the vector of the
constants in the linear
system.
5
1
7
3. Return to the Matrix
Catalog.
MATRIX
In this example, the
vector you created is
listed as M1.
4. Create a new matrix.
Select Real matrix
5. Enter the equation
coefficients.
2
4
1
3
1
1
1
4
2
In this example, the matrix you created is listed as
M2.
6. Return to HOME and enter the calculation to
coefficients matrix.
M2
–1
x
M1
The result is a vector of the
solutions x = 2, y = 3 and z = –2.
An alternative method, is to use the RREF function. See
“RREF” on page 15-12.
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Matrix functions and commands
About functions
•
Functions can be used in any aplet or in HOME. They
are listed in the MATH menu under the Matrix
category. They can be used in mathematical
expressions—primarily in HOME—as well as in
programs.
•
•
Functions always produce and display a result. They
do not change any stored variables, such as a matrix
variable.
Functions have arguments that are enclosed in
parentheses and separated by commas; for example,
CROSS(vector1,vector2). The matrix input can be
either a matrix variable name (such as M1) or the
actual matrix data inside brackets. For example,
CROSS(M1,[1,2]).
About commands
Matrix commands are listed in the CMDS menu (
CMDS), in the matrix category.
See “Matrix commands” on page 18-24 for details of the
matrix commands available for use in programming.
Functions differ from commands in that a function can be
used in an expression. Commands cannot be used in an
expression.
Argument conventions
•
For row# or column#, supply the number of the row
(counting from the top, starting with 1) or the number
of the column (counting from the left, starting with 1).
•
The argument matrix can refer to either a vector or a
matrix.
Matrix functions
COLNORM
Column Norm. Finds the maximum value (over all
columns) of the sums of the absolute values of all elements
in a column.
COLNORM(matrix)
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COND
Condition Number. Finds the 1-norm (column norm) of a
square matrix.
COND(matrix)
CROSS
DET
Cross Product of vector1 with vector2.
CROSS(vector1, vector2)
Determinant of a square matrix.
DET(matrix)
DOT
Dot Product of two arrays, matrix1 matrix2.
DOT(matrix1, matrix2)
EIGENVAL
EIGENVV
Displays the eigenvalues in vector form for matrix.
EIGENVAL(matrix)
Eigenvectors and Eigenvalues for a square matrix.
Displays a list of two arrays. The first contains the
eigenvectors and the second contains the eigenvalues.
EIGENVV(matrix)
IDENMAT
Identity matrix. Creates a square matrix of dimension
size × size whose diagonal elements are 1 and off-
diagonal elements are zero.
IDENMAT(size)
INVERSE
LQ
Inverts a square matrix (real or complex).
INVERSE(matrix)
LQ Factorization. Factors an m × n matrix into three
matrices:
{[[ m × n lowertrapezoidal]],[[ n × n orthogonal]],
[[ m × m permutation]]}.
LQ(matrix)
LSQ
Least Squares. Displays the minimum norm least squares
matrix (or vector).
LSQ(matrix1, matrix2)
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LU
LU Decomposition. Factors a square matrix into three
matrices:
{[[lowertriangular]],[[uppertriangular]],[[permutation]]}
The uppertriangular has ones on its diagonal.
LU(matrix)
MAKEMAT
Make Matrix. Creates a matrix of dimension rows ×
columns, using expression to calculate each element. If
expression contains the variables I and J, then the
calculation for each element substitutes the current row
number for I and the current column number for J.
MAKEMAT(expression, rows, columns)
Example
MAKEMAT(0,3,3)returns a 3×3 zero matrix,
[[0,0,0],[0,0,0],[0,0,0]].
QR
QR Factorization. Factors an m×n matrix into three
matrices: {[[m×m orthogonal]],[[m×n
uppertrapezoidal]],[[n×n permutation]]}.
QR(matrix)
RANK
Rank of a rectangular matrix.
RANK(matrix)
ROWNORM
Row Norm. Finds the maximum value (over all rows) for
the sums of the absolute values of all elements in a row.
ROWNORM(matrix)
RREF
Reduced-Row Echelon Form. Changes a rectangular
matrix to its reduced row-echelon form.
RREF(matrix)
SCHUR
Schur Decomposition. Factors a square matrix into two
matrices. If matrix is real, then the result is
{[[orthogonal]],[[upper-quasi triangular]]}.
If matrix is complex, then the result is
{[[unitary]],[[upper-triangular]]}.
SCHUR(matrix)
SIZE
Dimensions of matrix. Returned as a list: {rows,columns}.
SIZE(matrix)
15-12
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SPECNORM
SPECRAD
SVD
Spectral Norm of matrix.
SPECNORM(matrix)
Spectral Radius of a square matrix.
SPECRAD(matrix)
Singular Value Decomposition. Factors an m × n matrix
into two matrices and a vector:
{[[m × m square orthogonal]],[[n × n square orthogonal]],
[real]}.
SVD(matrix)
SVL
Singular Values. Returns a vector containing the singular
values of matrix.
SVL(matrix)
TRACE
Finds the trace of a square matrix. The trace is equal to
the sum of the diagonal elements. (It is also equal to the
sum of the eigenvalues.)
TRACE(matrix)
TRN
Transposes matrix. For a complex matrix, TRN finds the
conjugate transpose.
TRN(matrix)
Examples
Identity Matrix
You can create an identity matrix with the IDENMAT
function. For example, IDENMAT(2) creates the 2×2
identity matrix [[1,0],[0,1]].
You can also create an identity matrix using the
MAKEMAT (make matrix) function. For example, entering
MAKEMAT(I¼J,4,4) creates a 4 × 4 matrix showing the
numeral 1 for all elements except zeros on the diagonal.
The logical operator ¼ returns 0 when I (the row number)
and J (the column number) are equal, and returns 1 when
they are not equal.
Matrices
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Transposing a
Matrix
The TRN function swaps the row-column and column-row
elements of a matrix. For instance, element 1,2 (row 1,
column 2) is swapped with element 2,1; element 2,3 is
swapped with element 3,2; and so on.
For example, TRN([[1,2],[3,4]])creates the matrix
[[1,3],[2,4]].
Reduced-Row
Echelon Form
The following set of equations x – 2y + 3z = 14
2x + y – z = – 3
4x – 2y + 2z = 14
can be written as the augmented matrix
1 –2 3 14
2 1 –1 –3
4 –2 2 14
which can then stored as a
3 × 4 real matrix in any
matrix variable. M1 is used
in this example.
You can use the RREF
function to change this to
reduced row echelon form,
storing it in any matrix
variable. M2 is used in this
example.
The reduced row echelon
matrix gives the solution to
the linear equation in the
fourth column.
An advantage of using the
RREF function is that it will also work with inconsistent
matrices resulting from systems of equations which have
no solution or infinite solutions.
For example, the following set of equations has an infinite
number of solutions:
x + y – z = 5
2x – y = 7
x – 2y + z = 2
15-14
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The final row of zeros in the
reduced-row echelon form
of the augmented matrix
indicates an inconsistent
system with infinite
solutions.
Matrices
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16
Lists
You can do list operations in HOME and in programs. A
list consists of comma-separated real or complex
numbers, expressions, or matrices, all enclosed in braces.
A list may, for example, contain a sequence of real
numbers such as {1,2,3}. (If the Decimal Mark mode is
set to Comma, then the separators are periods.) Lists
represent a convenient way to group related objects.
There are ten list variables available, named L0 to L9. You
can use them in calculations or expressions in HOME or
in a program. Retrieve the list names from the VARS
menu, or just type their names from the keyboard.
You can create, edit, delete, send, and receive named
lists in the List catalog (
LIST). You can also create
and store lists—named or unnnamed—in HOME lists
List variables are identical in behaviour to the columns
C1.C0 in the Statistics aplet. You can store a statistics
column to a list (or vice versa) and use any of the list
functions on the statistics columns, or the statistics
functions, on the list variables.
Create a list in
the List Catalog
1. Open the List catalog.
LIST.
2. Highlight the list name
you want to assign to
the new list (L1, etc.)
and press
to
display the List editor.
Lists
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3. Enter the values you want in the list, pressing
after each one.
Values can be real or
complex numbers (or
an expression). If you
enter a calculation, it is
evaluated and the
result is inserted in the
list.
4. When done, press
LIST to see the List catalog,
or press
to return to HOME.
List catalog keys
The list catalog keys are:
Key
Meaning
Opens the highlighted list for
editing.
Transmits the highlighted list to
another hp 39gs or a PC. See
“Sending and receiving aplets” on
page 19-4 for further information.
Receives a list from another
hp 39gs or a PC. See “Sending and
receiving aplets” on page 19-4 for
further information.
Clears the highlighted list.
Clears all lists.
CLEAR
or Moves to the end or the beginning
of the catalog.
16-2
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List edit keys
When you press
to create or change a list, the
following keys are available to you:
Key
Meaning
Copies the highlighted list item into
the edit line.
Inserts a new value before the
highlighted item.
Deletes the highlighted item from
the list.
CLEAR
Clears all elements from the list.
or Moves to the end or the beginning
of the list.
Create a list in
HOME
1. Enter the list on the edit line. Start and end the list
with braces (the shifted and keys) and
separate each element with a comma.
2. Press
to evaluate and display the list.
Immediately after typing in the list, you can store it in
a variable by pressing
listname
. The
list variable names are L0 through L9.
This example stores the
list {25,147,8} in L1.
Note: You can omit the
final brace when
entering a list.
Lists
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Displaying and editing lists
To display a list
•
In the List catalog, highlight the list name and press
.
•
In HOME, enter the name of the list and press
.
To display one
element
In HOME, enter listname(element#). For example, if L2 is
{3,4,5,6}, then L2(2)
returns 4.
To edit a list
1. Open the List catalog.
LIST.
2. Press
or
to highlight the name of the list you
want to edit (L1, etc.) and press
list contents.
to display the
3. Press
or
to highlight the element you want to
edit. In this example, edit the third element so that it
has a value of 5.
5
4. Press
.
16-4
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To insertan element
in a list
1. Open the List catalog.
LIST.
2. Press
or
to
highlight the name of
the list you want to edit
(L1, etc.) and press
to display the list
contents.
New elements are inserted above the highlighted
position. In this example, an element, with the value
of 9, is inserted between the first and second
elements in the list.
3. Press
to the
insertion position, then
press
, and press
9.
4. Press
.
To store one
element
In HOME, enter value
example, to store 148 as the second element in L1, type
148 L1(2)
listname(element). For
.
Lists
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Deleting lists
To delete a list
In the List catalog, highlight the list name and press
.
You are prompted to confirm that you want to delete the
contents of the highlighted list variable. Press
delete the contents.
to
To delete all lists
In the List catalog, press
CLEAR.
Transmitting lists
You can send lists to calculators or PCs just as you can
aplets, programs, matrices, and notes.
connect the calculators using an appropriate cable).
2. Open the List catalogs on both calculators.
3. Highlight the list to send.
4. Press
and choose the method of sending
(infrared or cable).
5. Press
on the receiving calculator and choose
the method of receiving (infrared or cable).
For more information on sending and receiving files, see
“Sending and receiving aplets” on page 19-4.
List functions
List functions are found in the MATH menu. You can use
them in HOME, as well as in programs.
You can type in the name
of the function, or you can
copy the name of the
function from the List
category of the MATH
menu. Press
(the
alpha L character key). This
highlights the List category in the left column. Press
to
move the cursor to the right column which contain the List
functions, select a function, and press
.
List functions have the following syntax:
•
Functions have arguments that are enclosed in
parentheses and separated by commas. Example:
16-6
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CONCAT(L1,L2). An argument can be either a list
variable name (such as L1) or the actual list. For
example, REVERSE({1,2,3}).
•
If Decimal Mark in Modes is set to Comma, use
periods to separate arguments. For example,
CONCAT(L1.L2).
Common operators like +, –, ×, and / can take lists as
arguments. If there are two arguments and both are lists,
then the lists must have the same length, since the
calculation pairs the elements. If there are two arguments
and one is a real number, then the calculation pairs the
number with each element of the list.
Example
5*{1,2,3} returns {5,10,15}.
Besides the common operators that can take numbers,
matrices, or lists as arguments, there are commands that
can only operate on lists.
CONCAT
ΔLIST
Concatenates two lists into a new list.
CONCAT(list1,list2)
Example
CONCAT({1,2,3},{4})returns {1,2,3,4}.
Creates a new list composed of the first differences, that
is, the differences between the sequential elements in
list1. The new list has one fewer elements than list1. The
first differences for {x x ... x } are {x –x ... x –x }.
1
2
n
2
1
n
n–1
ΔLIST(list1)
Lists
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Example
In HOME, store {3,5,8,12,17,23} in L5 and find the first
differences for the list.
{3,5,8,12,17,23
}
L 5
L
Select ΔLIST
L5
MAKELIST
Calculates a sequence of elements for a new list.
Evaluates expression with variable from begin to end
values, taken at increment steps.
MAKELIST(expression,variable,begin,end,
increment)
The MAKELIST function generates a series by
automatically producing a list from the repeated
evaluation of an expression.
Example
In HOME, generate a series of squares from 23 to 27.
L
Select
MAKELIST
A
A
23
27
1
ΠLIST
Calculates the product of all elements in list.
ΠLIST(list)
Example
ΠLIST({2,3,4})returns 24.
POS
Returns the position of an element within a list. The
element can be a value, a variable, or an expression. If
there is more than one instance of the element, the
16-8
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position of the first occurrence is returned. A value of 0 is
returned if there is no occurrence of the specified element.
POS(list, element)
Example
POS ({3, 7, 12, 19},12)returns 3
REVERSE
SIZE
Creates a list by reversing the order of the elements in a
list.
REVERSE(list)
Calculates the number of elements in a list.
SIZE(list)
Also works with matrices.
ΣLIST
Calculates the sum of all elements in list.
ΣLIST(list)
Example
ΣLIST({2,3,4})returns 9.
SORT
Sorts elements in ascending order.
SORT(list)
Finding statistical values for list elements
To find values such as the mean, median, maximum, and
minimum values of the elements in a list, use the Statistics
aplet.
Example
In this example, use the Statistics aplet to find the mean,
median, maximum, and minimum values of the elements
in the list, L1.
1. Create L1 with values 88, 90, 89, 65, 70, and 89.
{ 88
65
}
90
70
89
89
L1
Lists
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2. In HOME, store L1 into
C1. You will then be
able to see the list data in the Numeric view of the
Statistics aplet.
L1
C1
3. Start the Statistics aplet, and select 1-variable mode
(press
, if necessary, to display
).
Select
Statistics
Note: Your list values are now in column 1 (C1).
4. In the Symbolic view, define H1 (for example) as C1
(sample) and 1 (frequency).
5. Go to the Numeric view to display calculated
statistics.
See “One-variable” on page 10-14 for the meaning
of each computed statistic.
16-10
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17
Notes and sketches
Introduction
The HP 39gs has text and picture editors for entering
notes and sketches.
•
Each aplet has its own independent Note view and
Sketch view. Notes and sketches that you create in
these views are associated with the aplet. When you
save the aplet, or send it to another calculator, the
notes and sketches are saved or sent as well.
•
The Notepad is a collection of notes independent of
all aplets. These notes can also be sent to another
calculator via the Notepad Catalog.
Aplet note view
You can attach text to an aplet in its Note view.
To write a note in
Note view
1. In an aplet, press NOTE for the Note view.
2. Use the note editing keys shown in the table in the
following section.
3. Set Alpha lock (
) for quick entry of letters. For
lowercase Alpha lock, press
.
4. While Alpha lock is on:
–
To type a single letter of the opposite case, press
letter.
–
To type a single non-alpha character (such as 5
or [ ), press
first. (This turns off Alpha
lock for one character.)
Your work is automatically saved. Press any view key
) or to exit
(
,
,
,
the Notes view.
Notes and sketches
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Note edit keys
Key
Meaning
Space key for text entry.
Displays next page of a multi-page
note.
Alpha-lock for letter entry.
Lower-case alpha-lock for letter
entry.
Backspaces cursor and deletes
character.
Deletes current character.
Starts a new line.
CLEAR
Erases the entire note.
Menu for entering variable names,
and contents of variables.
Menu for entering math
operations, and constants.
Menu for entering program
commands.
CMDS
Displays special characters. To
type one, highlight it and press
. To copy a character without
closing the CHARS screen, press
.
CHARS
17-2
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Aplet sketch view
You can attach pictures to an aplet in its Sketch view
SKETCH). Your work is automatically saved with the
(
aplet. Press any other view key or
Sketch view
to exit the
Sketch keys
Key
Meaning
Stores the specified portion of the
current sketch to a graphics
variable (G1 through G0).
Adds a new, blank page to the
current sketch set.
Displays next sketch in the sketch
set. Animates if held down.
Opens the edit line to type a text
label.
Displays the menu-key labels for
drawing.
Deletes the current sketch.
Erases the entire sketch set.
CLEAR
Toggles menu key labels on and
off. If menu key labels are hidden,
or any menu key, redisplays
the menu key labels.
To draw a line
1. In an aplet, press
2. In Sketch view, press
where you want to start the line
3. Press . This turns on line-drawing.
4. Move the cursor in any direction to the end point of
the line by pressing the keys.
5. Press to finish the line.
SKETCH for the Sketch view.
and move the cursor to
,
,
,
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To draw a box
1. In Sketch view, press
and move the cursor to
where you want any corner of the box to be.
2. Press
.
3. Move the cursor to mark the opposite corner for the
box. You can adjust the size of the box by moving the
cursor.
4. Press
to finish the box.
To draw a circle
DRAW keys
1. In Sketch view, press
and move the cursor to
where you want the center of the circle to be.
2. Press
. This turns on circle drawing.
3. Move the cursor the distance of the radius.
4. Press
to draw the circle.
Key
Meaning
Dot on. Turns pixels on as the cursor
moves.
Dot off. Turns pixels off as the cursor
moves.
Draws a line from the cursor’s starting
position to the cursor’s current position.
Press
when you have finished. You
can draw a line at any angle.
Draws a box from the cursor’s starting
position to the cursor’s current position.
Press
when you have finished.
Draws a circle with the cursor’s starting
position as the center. The radius is the
distance between the cursor’s starting
and ending position. Press
the circle.
to draw
17-4
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To label parts of a
sketch
1. Press
the Alpha shift on, press
(for lowercase).
To make the label a smaller character size, turn off
before pressing . ( is a toggle
and type the text on the edit line. To lock
(for uppercase) or
between small and large font size). The smaller
character size cannot display lowercase letters.
2. Press
.
3. Position the label where you want it by pressing the
,
4. Press
5. Press
,
,
keys.
again to affix the label.
to continue
drawing, or press
to exit the
Sketch view.
To create a set of
sketches
You can create a set of up to ten sketches. This allows for
simple animation.
•
After making a sketch, press
to add a new,
blank page. You can now make a new sketch, which
becomes part of the current set of sketches.
•
•
To view the next sketch in an existing set, press
. Hold
down for animation.
To remove the current page in the current sketch
series, press
.
To store into a
graphics variable
You can define a portion of a sketch inside a box, and
then store that graphic into a graphics variable.
1. In the Sketch view, display the sketch you want to
copy (store into a variable).
2. Press
3. Highlight the variable name you want to use and
press
4. Draw a box around the portion you want to copy:
move the cursor to one corner, press , then move
the cursor to the opposite corner, and press
.
.
.
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To import a
graphics variable
You can copy the contents of a graphics variable into the
Sketch view of an aplet.
1. Open the Sketch view of the aplet (
The graphic will be copied here.
SKETCH).
2. Press
,
.
3. Highlight Graphic, then press
name of the variable (G1, etc.).
and highlight the
4. Press
variable.
to recall the contents of the graphics
graphic, then press
The notepad
Subject to available memory, you can store as many
notes as you want in the Notepad (
NOTEPAD).
These notes are independent of any aplet. The Notepad
catalog lists the existing entries by name. It does not
include notes that were created in aplets’ Note views, but
these can be imported. See “To import a note” on
page 17-8.
To create a note in
the Notepad
1. Display the Notepad
catalog.
NOTEPAD
2. Create a new note.
3. Enter a name for your
note.
MYNOTE
17-6
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4. Write your note.
See “Note edit keys”
on page 17-2 for more
information on the
entry and editing of
notes.
5. When you are finished, press
or an aplet key
to exit Notepad. Your work is automatically saved.
Notepad Catalog keys
Key
Meaning
Opens the selected note for
editing.
Begins a new note, and asks
for a name.
Transmits the selected note to
another HP 39gs or PC.
Receives a note being
transmitted from another HP
39gs or PC.
Deletes the selected note.
CLEAR
Deletes all notes in the
catalog.
Notes and sketches
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To import a note
You can import a note from the Notepad into an aplet’s
Note view, and vice versa. Suppose you want to copy a
note named “Assignments” from the Notepad into the
Function Note view:
1. In the Function aplet, display the Note view
(
NOTE).
2. Press
, highlight Notepadin the left
column, then highlight the name “Assignments” in the
right column.
3. Press
to copy the contents of
“Assignments” to the Function Note view.
Note: To recall the name instead of the contents,
press
instead of
.
Suppose you want to copy the Note view from the current
aplet into the note, Assignments, in the Notepad.
1. In the Notepad (
“Assignments”.
NOTEPAD), open the note,
2. Press
, highlight Notein the left
and highlight NoteTextin
column, then press
the right column.
3. Press
to recall the contents of the Note
view into the note “Assignments”.
17-8
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18
Programming
Introduction
This chapter describes how to program using the hp
39gs. In this chapter you’ll learn about:
•
using the Program catalog to create and edit
programs
•
•
•
programming commands
storing and retrieving variables in programs
programming variables.
H I N T
More information on programming, including examples
and special tools, can be found at HP’s calculators web
site:
http://www.hp.com/calculators
The Contents of a
Program
An HP 39gs program contains a sequence of numbers,
mathematical expressions, and commands that execute
automatically to perform a task.
These items are separated by a colon ( : ). Commands
that take multiple arguments have those arguments
separated by a semicolon ( ; ). For example,
PIXON xposition;yposition:
Structured
Programming
Inside a program you can use branching structures to
control the execution flow. You can take advantage of
structured programming by creating building-block
programs. Each building-block program stands
alone—and it can be called from other programs. Note:
If a program has a space in its name then you have to put
quotes around it when you want to run it.
Programming
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Example
RUN GETVALUE: RUN CALCULATE: RUN
"SHOW ANSWER":
This program is separated into three main tasks, each an
individual program. Within each program, the task can
be simple—or it can be divided further into other
programs that perform smaller tasks.
Program catalog
The Program catalog is where you create, edit, delete,
send, receive, or run programs. This section describes
how to
•
open the Program catalog
create a new program
•
•
•
•
•
•
•
•
•
•
enter commands from the program commands menu
enter functions from the MATH menu
edit a program
run and debug a program
stop a program
copy a program
send and receive a program
delete a program or its contents
customize an aplet.
Open Program
Catalog
1. Press
PROGRM.
The Program Catalog displays a list of program
names. The Program Catalog contains a built-in entry
called Editline.
Editlinecontains the last expression that you
entered from the edit line in HOME, or the last data
you entered in an input form. (If you press
from HOME without entering any data, the HP 39gs
runs the contents of Editline.)
Before starting to work with programs, you should
take a few minutes to become familiar with the
Program catalog menu keys. You can use any of the
following keys (both menu and keyboard), to perform
tasks in the Program catalog.
18-2
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Program catalog keys
The program catalog keys are:
Key
Meaning
Opens the highlighted program
for editing.
Prompts for a new program
name, then opens an empty
program.
Transmits the highlighted
program to another HP 39gs or to
a disk drive.
Receives the highlighted program
from another HP 39gs or from a
disk drive.
Runs the highlighted program.
or
Moves to the beginning or end of
the Program catalog.
Deletes the highlighted program.
CLEAR
Deletes all programs in the
program catalog.
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18-3
Creating and editing programs
Create a new
program
1. Press
2. Press
PROGRM to open the Program catalog.
.
The HP 39gs prompts
you for a name.
A program name can contain special characters,
such as a space. However, if you use special
characters and then run the program by typing it in
HOME, you must enclose the program name in
double quotes (" "). Don't use the " symbol within your
program name.
3. Type your program
name, then press
.
When you press
the Program Editor
opens.
,
4. Enter your program. When done, start any other
activity. Your work is saved automatically.
Entercommands
Until you become familiar with the HP 39gs commands,
the easiest way to enter commands is to select them from
the Commands menu from the Program editor. You can
also type in commands using alpha characters.
1. From the Program editor, press
the Program Commands menu.
CMDS to open
CMDS
18-4
Programming
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2. On the left, use
category, then press
or
to highlight a command
to access the commands in
the category. Select the command that you want.
3. Press
to paste the command into the program
editor.
Edit a program
1. Press
PROGRM to
open the Program
catalog.
2. Use the arrow keys to highlight the program you want
to edit, and press . The HP 39gs opens the
Program Editor. The name of your program appears
in the title bar of the display. You can use the
following keys to edit your program.
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Editing keys
The editing keys are:
Key Meaning
Inserts the
editing point.
character at the
Inserts space into text.
Displays previous page of the
program.
Displays next page of the program.
Moves up or down one line.
Moves right or left one character.
Alpha-lock for letter entry. Press
A...Z to lock lower case.
Backspaces cursor and deletes
character.
Deletes current character.
Starts a new line.
CLEAR
Erases the entire program.
Displays menus for selecting variable
names, contents of variables, math
functions, and program constants.
CMDS
Displays menus for selecting program
conmmands.
CHARS
Displays all characters. To type one,
highlight it and press
.
To enter several characters in a row,
use the
CHARS menu.
menu key while in the
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Using programs
Run a program
From HOME, type RUN program_name.
or
From the Program catalog, highlight the program you
want to run and press
Regardless of where you start the program, all programs
run in HOME. What you see will differ slightly depending
on where you started the program. If you start the
program from HOME, the HP 39gs displays the contents
of Ans (Home variable containing the last result), when
the program has finished. If you start the program from
the Program catalog, the hp39gs returns you to the
Program catalog when the program ends.
Debug a
program
If you run a program that contains errors, the program
will stop and you will see an error message.
To debug the program:
1. Press
to edit the program.
The insert cursor appears in the program at the point
where the error occurred.
2. Edit the program to fix the error.
3. Run the program.
4. Repeat the process until you correct all errors.
Stop a program
You can stop the running of a program at any time by
pressing CANCEL (the
key). Note: You may have to
press it a couple of times.
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Copy a program You can use the following procedure if you want to make
a copy of your work before editing—or if you want to use
one program as a template for another.
1. Press
2. Press
PROGRM to open the Program catalog.
.
3. Type a new file name, then choose
.
The Program Editor opens with a new program.
4. Press
to open the variables menu.
to quickly scroll to Program.
5. Press
6. Press
copy.
, then highlight the program you want to
7. Press
, then press
.
The contents of the highlighted program are copied
into the current program at the cursor location.
H I N T
If you use a programming routine often, save the routine
under a different program name, then use the above
method to copy it into your programs.
Transmit a
program
You can send programs to, and receive programs from,
other calculators just as you can send and receive aplets,
matrices, lists, and notes.
After aligning the calculators’ infrared ports, open the
Program catalogs on both calculators. Highlight the
program to send, then press
on the sending
calculator and on the receiving calculator.
You can also send programs to, and receive programs
from, a remote storage device (aplet disk drive or
computer). This takes place via a cable connection and
requires an aplet disk drive or specialized software
running on a PC (such as a connectivity kit).
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Delete a
program
To delete a program:
1. Press
PROGRM to open the Program catalog.
2. Highlight a program to delete, then press
.
Delete all
programs
You can delete all programs at once.
1. In the Program catalog, press
2. Press
CLEAR.
.
Delete the
contents of a
program
You can clear the contents of a program without deleting
the program name.
1. Press
2. Highlight a program, then press
3. Press CLEAR, then press
PROGRM to open the Program catalog.
.
.
4. The contents of the program are deleted, but the
program name remains.
Customizing an aplet
You can customize an aplet and develop a set of
programs to work with the aplet.
Use the SETVIEWS command to create a custom VIEWS
menu which links specially written programs to the new
aplet.
A useful method for customizing an aplet is illustrated
below:
1. Decide on the built-in aplet that you want to
customize. For example you could customize the
Function aplet or the Statistics aplet. The customized
aplet inherits all the properties of the built-in aplet.
Save the customized aplet with a unique name.
2. Customize the new aplet if you need to, for example
by presetting axes or angle measures.
3. Develop the programs to work with your customized
aplet. When you develop the aplet’s programs, use
the standard aplet naming convention. This allows
you to keep track of the programs in the Program
catalog that belong to each aplet. See “Aplet naming
convention” on page 18-10.
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18-9
4. Develop a program that uses the SETVIEWS
command to modify the aplet’s VIEWS menu. The
menu options provide links to associated programs.
You can specify any other programs that you want
transferred with the aplet. See “SETVIEWS” on page
18-14 for information on the command.
5. Ensure that the customized aplet is selected, then run
the menu configuration program to configure the
aplet’s VIEWS menu.
6. Test the customized aplet and debug the associated
programs. (Refer to “Debug a program” on page
16-7).
Aplet naming convention
To assist users in keeping track of aplets and associated
programs, use the following naming convention when
setting up an aplet’s programs:
•
Start all program names with an abbreviation of the
aplet name. We will use APL in this example.
•
Name programs called by menu entries in the VIEWS
menu number, after the entry, for example:
–
APL.ME1 for the program called by menu option
1
–
APL.ME2 for the program called by menu option
2
•
Name the program that configures the new VIEWS
menu option APL.SV where SV stands for SETVIEWS.
For example, a customized aplet called “Differentiation”
might call programs called DIFF.ME1, DIFF.ME2, and
DIFF.SV.
Example
This example aplet is designed to demonstrate the
process of customizing an aplet. The new aplet is based
on the Function aplet. Note: This aplet is not intended to
serve a serious use, merely to illustrate the process.
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Save the aplet
1. Open the Function aplet and save it as
“EXPERIMENT”. The new aplet appears in the Aplet
library.
Select
Function
EXPERIMENT
2. Create a program
called EXP.ME1 with
contents as shown. This
program configures the
plot ranges, then runs a
program that allows
you to set the angle format.
3. Create a program
called EXP.ME2 with
contents as shown. This
program sets the
numeric view options
for the aplet, and runs
the program that you can use to configure the angle
mode.
4. Create a program
called EXP.ANG which
the previous two
programs call.
5. Create a program
called EXP.S which runs
when you start the
aplet, as shown. This
program sets the angle
mode to degrees, and
sets up the initial function that the aplet plots.
Configuring the
Setviews menu
option
In this section we will begin by configuring the
VIEWS menu by using the SETVIEWS command. We
will then create the “helper” programs called by the
VIEWS menu which will do the actual work.
programs
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6. Open the Program catalog and create a program
named “EXP.SV”. Include the following code in the
program.
Each entry line after the command SETVIEWS is a trio
that consists of a VIEWS menu text line (a space
indicates none), a program name, and a number that
defines the view to go to after the program has run its
course. All programs listed here will transfer with an
aplet when the aplet is transferred.
SETVIEWS ’’’’;’’’’;18;
Sets the first menu option to be “Auto
scale”. This is the fourth standard Function
aplet view menu option and the 18 “Auto
scale”, specifies that it is to be included in
the new menu. The empty quotes will
ensure that the old name of “Auto scale”
appears on the new menu. See
“SETVIEWS” on page 18-14.
’’My Entry1’’;’’EXP.ME1’’;1;
Sets the second menu option. This option
runs program EXP.ME1, then returns to
view 1, Plot view.
’’My Entry2’’;’’EXP.ME2’’;3;
Sets the third menu option. This option
runs the program EXP.ME2, then returns to
view 3, the NUM view.
’’’’;’’EXP.SV’’;0;
This line specifies that the program to set
the View menu (this program) is
transferred with the aplet. The space
character between the first set of quotes in
the trio specifies that no menu option
appears for the entry. You do not need to
transfer this program with the aplet, but it
allows users to modify the aplet’s menu if
they want to.
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’’’’;’’EXP.ANG’’;0;
The program EXP.ANG is a small routine
that is called by other programs that the
aplet uses. This entry specifies that the
program EXP.ANGis transferred when the
aplet is transferred, but the space in the
first quotes ensures that no entry appears
on the menu.
’’Start’’;’’EXP.S’’;7:
This specifies the Start menu option. The
program that is associated with this entry,
EXP.S, runs automatically when you
start the aplet. Because this menu option
specifies view 7, the VIEWS menu opens
when you start the aplet.
You only need to run this program once to configure
your aplet’s VIEWS menu. Once the aplet’s VIEWS
menu is configured, it remains that way until you run
SETVIEWS again.
You do not need to include this program for your
aplet to work, but it is useful to specify that the
program is attached to the aplet, and transmitted
when the aplet is transmitted.
7. Return to the program
catalog. The programs
that you created should
appear as follows:
8. You must now
the
program EXP.SV to execute the SETVIEWS command
and create the modified VIEWS menu. Check that the
name of the new aplet is highlighted in the Aplet
view.
9. You can now return to the Aplet library and press
to run your new aplet.
Programming commands
This section describes the commands for programming
with hp 39GS. You can enter these commands in your
program by typing them or by accessing them from the
Commands menu.
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18-13
Aplet commands
CHECK
Checks (selects) the corresponding function in the current
aplet. For example, Check 3 would check F3 if the current
aplet is Function. Then a checkmark would appear next
and evaluated in Numeric view.
CHECKn:
SELECT
Selects the named aplet and makes it the current aplet.
Note: Quotes are needed if the name contains spaces or
other special characters.
SELECTapletname:
SETVIEWS
The SETVIEWS command is used to define entries in the
VIEWS menu for aplets that you customize. See
“Customizing an aplet” on page 18-9 for an example of
using the SETVIEWS command.
When you use the SETVIEWS command, the aplet’s
standard VIEWS menu is deleted and the customized
menu is used in its place. You only need to apply the
command to an aplet once. The VIEWS menu changes
remain unless you apply the command again.
Typically, you develop a program that uses the
SETVIEWS command only. The command contains a trio
of arguments for each menu option to create, or program
to attach. Keep the following points in mind when using
this command:
•
The SETVIEWS command deletes an aplet’s standard
Views menu options. If you want to use any of the
standard options on your reconfigured VIEWS menu,
you must include them in the configuration.
•
When you invoke the SETVIEWS command, the
changes to an aplet’s VIEWS menu remain with the
aplet. You need to invoke the command on the aplet
again to change the VIEWS menu.
•
•
All the programs that are called from the VIEWS
menu are transferred when the aplet is transferred, for
example to another calculator or to a PC.
As part of the VIEWS menu configuration, you can
specify programs that you want transferred with the
aplet, but are not called as menu options. For
example, these can be sub-programs that menu
18-14
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options use, or the program that defines the aplet’s
VIEWS menu.
•
You can include a “Start” option in the VIEWS menu
to specify a program that you want to run
automatically when the aplet starts. This program
typically sets up the aplet’s initial configuration. The
START option on the menu is also useful for resetting
the aplet.
Command syntax
The syntax for the command is as follows:
SETVIEWS
"Prompt1";"ProgramName1";ViewNumber1;
"Prompt2";"ProgramName2";ViewNumber2:
(You can repeat as many Prompt/ProgramName/
ViewNumber trios of arguments as you like.)
Within each Prompt/ProgramName/ViewNumber trio,
you separate each item with a semi-colon.
Prompt
Prompt is the text that is displayed for the corresponding
entry in the Views menu. Enclose the prompt text in
double quotes.
Associating programs with your aplet
If Prompt consists of a single space, then no entry appears
in the view menu. The program specified in the
ProgramName item is associated with the aplet and
transferred whenever the aplet is transmitted. Typically,
you do this if you want to transfer the Setviews program
with the aplet, or you want to transfer a sub-program that
other menu programs use.
Auto-run programs
If the Prompt item is “Start”, then the ProgramName
program runs whenever you start the aplet. This is useful
for setting up a program to configure the aplet. Users can
select the Start item from the VIEWS menu to reset the
aplet if they change configurations.
You can also define a menu item called “Reset” which is
auto-run if the user chooses the
view.
button in the APLET
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18-15
ProgramName
ProgramName is the name of the program that runs when
the corresponding menu entry is selected. All programs
that are identified in the aplet’s SETVIEWS command are
transferred when the aplet is transmitted.
ViewNumber
ViewNumber is the number of a view to start after the
program finishes running. For example, if you want the
menu option to display the Plot view when the associated
program finishes, you would specify 1 as the
ViewNumber value.
Including standard menu options
To include one of an aplet’s standard VIEWS menu
options in your customized menu, set up the arguments
trio as follows:
•
•
•
The first argument specifies the menu item name:
–
Leave the argument empty to use the standard
Views menu name for the item, or
–
Enter a menu item name to replace the standard
name.
The second argument specifies the program to run:
–
Leave the argument empty to run the standard
menu option.
–
Insert a program name to run the program before
the standard menu option is executed.
The third argument specifies the view and the menu
number for the item. Determine the menu number
from the View numbers table below.
Note: SETVIEWS with no arguments resets the views
to default of the base aplet.
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View numbers
The Function aplet views are numbered as follows:
0
1
2
3
4
5
6
7
8
9
10
HOME
11
12
13
14
15
16
17
18
19
20
21
List Catalog
Matrix Catalog
Notepad Catalog
Program Catalog
Plot-Detail
Plot
Symbolic
Numeric
Plot-Setup
Symbolic-Setup
Numeric-Setup
Views
Plot-Table
Overlay Plot
Auto scale
Decimal
Note
Sketch view
Aplet Catalog
Integer
Trig
View numbers from 15 on will vary according to the
parent aplet. The list shown above is for the Function
aplet. Whatever the normal VIEWS menu for the parent
aplet, the first entry will become number 15, the second
number 16 and so on.
UNCHECK
Unchecks (unselects) the corresponding function in the
current aplet. For example, Uncheck 3 would uncheck F3
if the current aplet is Function.
UNCHECKn:
Branch commands
Branch commands let a program make a decision based
on the result of one or more tests. Unlike the other
programming commands, the branch commands work in
logical groups. Therefore, the commands are described
together rather than each independently.
IF...THEN...END
Executes a sequence of commands in the true-clause only
if the test-clause evaluates to true. Its syntax is:
IFtest-clause
THENtrue-clause END
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Example
1ꢂA :
IF A==1
THEN MSGBOX " A EQUALS 1" :
END:
IF... THEN... ELSE...
END
Executes the true-clause sequence of commands if the test-
clause is true, or the false-clause sequence of commands
if the test-clause is false.
IF test-clause
THEN true-clause ELSE false-clause END
Example
1ꢂA :
IF A==1 THEN
MSGBOX "A EQUALS 1" :
ELSE
MSGBOX "A IS NOT EQUAL TO 1" :
END:
CASE...END
Executes a series of test-clause commands that execute
the appropriate true-clause sequence of commands. Its
syntax is:
CASE
IF test-clause THEN true-clause END
1
1
IF test-clause THEN true-clause END
2
2
.
.
.
IF test-clause THEN true-clause END
n
n
END:
When CASE is executed, test-clause is evaluated. If the
1
test is true, true-clause is executed, and execution skips
1
to END. If test-clause if false, execution proceeds to test-
1
clause . Execution with the CASE structure continues until
2
a true-clause is executed (or until all the test-clauses
evaluate to false).
IFERR...
THEN...
ELSE…
END...
Many conditions are automatically recognized by the HP
39gs as error conditions and are automatically treated as
errors in programs.
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IFERR...THEN...ELSE…END allows a program to intercept
error conditions that otherwise would cause the program
to abort. Its syntax is:
IFERR trap-clause
THEN clause_1
ELSE clause_2
END:
Example
IFERR
60/X ꢂ Y:
THEN
MSGBOX "Error: X is zero.":
ELSE
MSGBOX "Value is "Y:
END:
RUN
Runs the named program. If your program name contains
special characters, such as a space, then you must
enclose the file name in double quotes (" ").
RUN"program name":or RUNprogramname:
STOP
Stops the current program.
STOP:
Drawing commands
The drawing commands act on the display. The scale of
the display depends on the current aplet's Xmin, Xmax,
Ymin, and Ymax values. The following examples assume
the hp 39gs default settings with the Function aplet as the
current aplet.
ARC
Draws a circular arc, of given radius, whose centre is at
(x,y) The arc is drawn from start_angle_measurement, to
end_angle_measurement.
ARCx;y;radius;start_angle_measurement;
end_angle_measurement:
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Example
ARC0;0;2;0;2π:
FREEZE:
Draws a circle centered
at (0,0) of radius 2. The
FREEZE command
causes the circle to
remain displayed on the screen until you press a key.
BOX
Draws a box with diagonally opposite corners (x1,y1) and
(x2,y2).
BOXx1;y1;x2;y2:
Example
BOX -1;-1;1;1:
FREEZE:
Draws a box, lower
corner at (–1,–1),
upper corner at (1,1)
ERASE
Clears the display
ERASE:
FREEZE
LINE
Halts the program, freezing the current display.
Execution resumes when any key is pressed.
Draws a line from (x1, y1) to (x2, y2).
LINEx1;y1;x2;y2:
PIXOFF
PIXON
TLINE
Turns off the pixel at the specified coordinates (x,y).
PIXOFFx;y:
Turns on the pixel at the specified coordinates (x,y).
PIXONx;y:
Toggles the pixels along the line from (x1, y1) to (x2, y2)
on and off. Any pixel that was turned off, is turned on;
any pixel that was turned on, is turned off. TLINE can be
used to erase a line.
TLINEx1;y1;x2;y2:
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Example
TLINE 0;0;3;3:
Erases previously drawn 45 degree line from (0,0) to
(3,3), or draws that line if it doesn’t already exist.
Graphic commands
The graphic commands use the graphics variables G0
through G9—or the Page variable from Sketch—as
graphicname arguments. The position argument takes the
form (x,y). Position coordinates depend on the current
aplet’s scale, which is specified by Xmin, Xmax, Ymin,
and Ymax. The upper left corner of the target graphic
(graphic2) is at (Xmin,Ymax).
You can capture the current display and store it in G0 by
simultaneously pressing
+
.
DISPLAY→
→DISPLAY
Stores the current display in graphicname.
DISPLAY→ graphicname:
Displays graphic from graphicname in the display.
→DISPLAY graphicname:
→GROB
Creates a graphic from expression, using font_size, and
stores the resulting graphic in graphicname. Font sizes
are 1, 2, or 3. If the fontsize argument is 0, the HP 39gs
creates a graphic display like that created by the SHOW
operation.
→GROB graphicname;expression;fontsize:
GROBNOT
GROBOR
Replaces graphic in graphicname with bitwise-inverted
graphic.
GROBNOT graphicname:
Using the logical OR, superimposes graphicname2 onto
graphicname1. The upper left corner of graphicname2 is
placed at position.
GROBORgraphicname1;(position);graphicname2:
Example
GROBOR G0; (1,1); G1:
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will superimpose G1 onto G0 starting a position (1,1),
where the position is given in terms of the current axes
settings, not as a pixel position.
GROBXOR
Using the logical XOR, superimposes graphicname2 onto
graphicname1. The upper left corner of graphicname2 is
placed at position.
GROBXOR
graphicname1;(position);graphicname2:
MAKEGROB
Creates graphic with given width, height, and
hexadecimal data, and stores it in graphicname.
MAKEGROB graphicname;width;height;hexdata:
PLOT→
Stores the Plot view display as a graphic in graphicname.
PLOT→ graphicname:
PLOT→ and DISPLAY→ can be used to transfer a copy
of the current PLOT view into the sketch view of the aplet
for later use and editing.
Example
1 ꢂ PageNum:
PLOT→ Page:
→ DISPLAY Page:
FREEZE:
This program stores the current PLOT view to the first page
in the sketch view of the current aplet and then displays
the sketch as a graphic object until any key is pressed.
→PLOT
Puts graph from graphicname into the Plot view display.
→PLOTgraphicname:
REPLACE
Replaces portion of graphic in graphicname1 with
graphicname2,starting at position.REPLACEalso
works for lists and matrices.
REPLACE
graphicname1;(position);graphicname2:
SUB
Extracts a portion of the named graphic (or list or matrix),
and stores it in a new variable, name. The portion is
specified by position and positions.
SUBname;graphicname;(position);(positions):
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ZEROGROB
Creates a blank graphic with given width and height,
and stores it in graphicname.
ZEROGROB graphicname;width;height:
Loop commands
Loop hp allow a program to execute a routine repeatedly.
The HP 39gs has three loop structures. The example
programs below illustrate each of these structures
incrementing the variable A from 1 to 12.
DO…UNTIL …END Do... Until... Endis a loop command that executes the
loop-clause repeatedly until test-clause returns a true
(nonzero) result. Because the test is executed after the
loop-clause, the loop-clause is always executed at least
once. Its syntax is:
DO loop-clause UNTIL test-clause END
1 ꢂ A:
DO
A + 1 ꢂ A
DISP 3;A:
UNTIL A == 12 END:
WHILE…
REPEAT…
END
While... Repeat... Endis a loop command that
repeatedly evaluates test-clause and executes loop-clause
sequence if the test is true. Because the test-clause is
executed before the loop-clause, the loop-clause is not
executed if the test is initially false. Its syntax is:
WHILEtest-clause REPEAT loop-clause END
1ꢂA:
WHILE A < 12 REPEAT
A+1 ꢂA
DISP 3;A:
END:
FOR…TO…STEP
...END
FOR name=start-expression TO end-expression
[STEP increment];
loop-clause END
FOR A=1 TO 12 STEP 1;
DISP 3;A:
END:
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Note that the STEP parameter is optional. If it is omitted,
a step value of 1 is assumed.
BREAK
Terminates loop.
BREAK:
Matrix commands
The matrix commands take variables M0–M9 as
arguments.
ADDCOL
Add Column. Inserts values into a column before
column_number in the specified matrix. You enter the
values as a vector. The values must be separated by
commas and the number of values must be the same as
the number of rows in the matrix name.
ADDCOL
name;[value ,...,value ];column_number:
1
n
ADDROW
Add Row. Inserts values into a row before row_number in
the specified matrix. You enter the values as a vector. The
values must be separated by commas and the number of
values must be the same as the number of columns in the
matrix name.
ADDROW name;[value ,..., value ];row_number:
1
n
DELCOL
Delete Column. Deletes the specified column from the
specified matrix.
DELCOL name;column_number:
DELROW
EDITMAT
Delete Row. Deletes the specified row from the specified
matrix.
DELROWname;row_number:
Starts the Matrix Editor and displays the specified matrix.
If used in programming, returns to the program when user
presses
.
EDITMATname:
18-24
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RANDMAT
Creates random matrix with a specified number of rows
and columns and stores the result in name
(name must be M0...M9). The entries will be integers
ranging from –9 to 9.
RANDMATname;rows;columns:
REDIM
Redimensions the specified matrix or vector to size. For a
matrix, size is a list of two integers {n1,n2}. For a vector,
size is a list containing one integer {n}.
REDIMname;size:
REPLACE
Replaces portion of a matrix or vector stored in name with
an object starting at position start. start for a matrix is a
list containing two numbers; for a vector, it is a single
number. Replace also works with lists and graphics.
REPLACEname;start;object:
SCALE
Multiplies the specified row_number of the specified
matrix by value.
SCALEname;value;rownumber:
SCALEADD
SUB
Multiplies the row of the matrix name by value, then adds
this result to the second specified row.
SCALEADDname;value;row1;row2:
Extracts a sub-object—a portion of a list, matrix, or
graphic from object—and stores it into name. start and
end are each specified using a list with two numbers for
a matrix, a number for vector or lists, or an ordered pair,
(X,Y), for graphics.
SUBname;object;start;end:
SWAPCOL
Swaps Columns. Exchanges column1 and column2 of the
specified matrix.
SWAPCOL name;column1;column2:
SWAPROW
Swap Rows. Exchanges row1 and row2 in the specified
matrix.
SWAPROWname;row1;row2:
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Print commands
These commands print to an HP infrared printer, for
example the HP 82240B printer.
PRDISPLAY
PRHISTORY
PRVAR
Prints the contents of the display.
PRDISPLAY:
Prints all objects in the history.
PRHISTORY:
Prints name and contents of variablename.
PRVARvariablename:
You can also use the PRVAR command to print the
contents of a program or a note.
PRVARprogramname;PROG:
PRVARnotename;NOTE:
Prompt commands
BEEP
Beeps at the frequency and for the time you specify.
BEEPfrequency;seconds:
CHOOSE
Creates a choose box, which is a box containing a list of
options from which the user chooses one. Each option is
numbered, 1 through n. The result of the choose
command is to store the number of the option chosen in a
variable. The syntax is
CHOOSEvariable_name;title;option ;option ;
1
2
...option :
n
where variable_name is the number of the option that will
be highlighted by default whenever the choose box is
displayed, title is the text displayed in the title bar of the
choose box, and option ...option are the options listed
1
n
in the choose box.
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Example
3 ꢂA:CHOOSE A;
"COMIC STRIPS";
"DILBERT";
"CALVIN&HOBBES";
"BLONDIE":
CLRVAR
Clears the specified variable. The syntax is:
CLRVAR variable :
Example
If you have stored
{1,2,3,4} in variable L1,
entering CLVAR L1
will clear L1.
DISP
Displays textitem in a row of the display at the
line_number. A text item consists of any number of
expressions and quoted strings of text. The expressions
are evaluated and turned into strings. Lines are numbered
from the top of the screen, 1 being the top and 7 being
the bottom.
DISP line_number;textitem:
Example
DISP 3;"A is" 2+2
Result: A is 4
(displayed on line 3)
DISPXY
Displays object at position (x_pos, y_pos) in size font. The
syntax is:
DISPXY x_pos;y_pos;font;object:
The value of object can be a text string, a variable, or a
combination of both. x_pos and y_pos are relative to the
current settings of Xmin, Xmax, Ymin and Ymax (which
you set in the PLOT SETUP view). The value of font is either
1 (small) or 2 (large).
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Example
DISPXY
–3.5;1.5;2;"HELLO
WORLD":
DISPTIME
Displays the current date and time.
DISPTIME
To set the date and time, simply store the correct settings
in the date and time variables. Use the following formats:
M.DDYYYY for the date and H.MMSSfor the time.
Examples
5.152000ꢂDATE(sets the date to May 15, 2000).
10.1500ꢂTIME(sets the time to 10:15 am).
EDITMAT
Matrix Editor. Opens the Matrix editor for the specified
matrix. Returns to the program when user presses
EDITMAT matrixname:
The EDITMAT command can also be used to create
matrices.
1. Press
2. Press
CMDS
M 1, and then press
.
The Matrix catalog opens with M1 available for
editing.
EDITMAT matrixname is an alternative to opening
the matrix editor with matrixname.
FREEZE
This command prevents the display from being updated
after the program runs. This allows you to view the
graphics created by the program. Cancel FREEZEby
pressing any key.
FREEZE:
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GETKEY
INPUT
Waits for a key, then stores the keycode rc.p in name,
where r is row number, c is column number, and p is key-
plane number. The key-planes numbers are: 1 for
unshifted; 2 for shifted; 4 for alpha-shifted; and 5 for both
alpha-shifted and shifted.
GETKEYname:
Creates an input form with a title bar and one field. The
field has a label and a default value. There is text help at
the bottom of the form. The user enters a value and
presses the
menu key. The value that the user enters
is stored in the variable name. The title, label, and help
items are text strings and need to be enclosed in double
quotes.
Use
CHARS to type the quote marks " ".
INPUTname;title,label;help;default:
Example
INPUT R; "Circular Area";
"Radius";
"Enter Number";1:
MSGBOX
Displays a message box containing textitem. A text item
consists of any number of expressions and quoted strings
of text. The expressions are evaluated and turned into
strings of text.
For example, "AREA IS:"2+2becomes AREA IS:4.
Use
CHARS to type the quote marks " ".
MSGBOXtextitem:
Example
1ꢂA:
MSGBOX "AREA IS: "π*A^2:
You can also use the NoteText variable to provide text
arguments. This can be used to insert line breaks. For
example, press
NOTE and type AREAIS
.
The position line
MSGBOXNoteText " " π*A^2:
will display the same message box as the previous
example.
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PROMPT
WAIT
Displays an input box with name as the title, and prompts
for a value for name. name can be a variable such as
A…Z, θ, L1…l9, C1…C9 or Z1…Z9.
PROMPTname:
Halts program execution for the specified number of
seconds.
WAITseconds:
Stat-One and Stat-Two commands
The following commands are used for analyzing one-
variable and two-variable statistical data.
Stat-One commands
DO1VSTATS
Calculates STATS using datasetname and stores the
results in the corresponding variables: NΣ, TotΣ, MeanΣ,
PVarΣ, SVarΣ, PSDev, SSDev, MinΣ, Q1, Median, Q3,
and MaxΣ. Datasetname can be H1, H2, ..., or H5.
Datasetname must include at least two data points.
DO1VSTATSdatasetname:
SETFREQ
Sets datasetname frequency according to column or
value. Datasetname can be H1, H2,..., or H5, column
can be C0–C9 and value can be any positive integer.
SETFREQdatasetname;column:
or
SETFREQdefinition;value:
SETSAMPLE
Sets datasetname sample according to column.
Datasetname can be H1–H5, and column can be
CO–C9.
SETSAMPLEdatasetname;column:
Stat-Two commands
DO2VSTATS
Calculates STATS using datasetname and stores the
results in corresponding variables: MeanX, ΣX, ΣX2,
MeanY, ΣY, ΣY2, ΣXY, Corr, PCov, SCov, and RELERR.
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Datasetname can be SI, S2,..., or S5. Datasetname must
include at least two pairs of data points.
DO2VSTATSdatasetname:
SETDEPEND
SETINDEP
Sets datasetname dependent column. Datasetname can
be S1, S2, …, or S5 and column can be C0–C9.
SETDEPENDdatasetname;column:
Sets datasetname independent column. Datasetname can
be S1, S2,…, or S5 and column can be C0–C9.
SETINDEPdatasetname;column:
Storing and retrieving variables in programs
variables. Home variables are used for real numbers,
complex numbers, graphics, lists, and matrices. Home
variables keep the same values in HOME and in aplets.
Aplet variables are those whose values depend on the
current aplet. The aplet variables are used in
programming to emulate the definitions and settings you
make when working with aplets interactively.
You use the Variable menu (
) to retrieve either
Home variables or aplet variables. See “The VARS menu”
on page 14-4. Not all variables are available in every
aplet. S1fit–S5fit, for example, are only available in the
Statistics aplet. Under each variable name is a list of the
aplets where the variable can be used.
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18-31
Plot-view variables
Area
Function
Contains the last value found by the Area function in Plot-
FCN menu.
Axes
All Aplets
Turns axes on or off.
From Plot Setup, check (or uncheck) AXES.
or
In a program, type:
1 ꢂ Axes—to turn axes on (default).
0 ꢂ Axes—to turn axes off.
Connect
Function
Parametric
Polar
Draws lines between successively plotted points.
From Plot Setup, check (or uncheck) CONNECT.
or
Solve
In a program, type
Statistics
1 ꢂ Connect—to connect plotted points (default,
except in Statistics where the default is off).
0 ꢂ Connect—not to connect plotted points.
Coord
Turns the coordinate-display mode in Plot view on or off.
Function
Parametric
Polar
Sequence
Solve
From Plot view, use the Menu mean key to toggle
coordinate display on an off.
In a program, type
1 ꢂCoord—to turn coordinate display on (default).
0 ꢂCoord—to turn coordinate display off.
Statistics
Extremum
Function
Contains the last value found by the Extremum operation
in the Plot-FCN menu.
FastRes
Function
Solve
Toggles resolution between plotting in every other column
(faster), or plotting in every column (more detail).
From Plot Setup, choose Faster or More Detail.
or
In a program, type
1 ꢂFastRes—for faster.
0 ꢂFastRes—for more detail (default).
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Grid
All Aplets
Turns the background grid in Plot view on or off. From Plot
setup, check (or uncheck) GRID.
or
In a program, type
1 ꢂGridto turn the grid on.
0 ꢂ Gridto turn the grid off (default).
Hmin/Hmax
Statistics
Defines minimum and maximum values for histogram
bars.
From Plot Setup for one-variable statistics, set values for
HRNG.
or
In a program, type
n1 ꢂHmin
n2 ꢂHmax
where n2 > n1
Hwidth
Statistics
Sets the width of histogram bars.
From Plot Setup in 1VAR stats set a value for Hwidth
or
In a program, type
nꢂHwidth
Indep
All Aplets
Defines the value of the independent variable used in
tracing mode.
In a program, type
nꢂIndep
InvCross
All Aplets
Toggles between solid crosshairs or inverted crosshairs.
(Inverted is useful if the background is solid).
From Plot Setup, check (or uncheck) InvCross
or
In a program, type:
1 ꢂ InvCross—to invert the crosshairs.
0 ꢂ InvCross—for solid crosshairs (default).
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Isect
Function
Contains the last value found by the Intersection function
in the Plot-FCN menu.
Labels
All Aplets
Draws labels in Plot view showing X and Y ranges.
From Plot Setup, check (or uncheck) Labels
or
In a program, type
1 ꢂLabels—to turn labels on.
0 ꢂLabels—to turn labels off (default).
Nmin / Nmax
Sequence
Defines the minimum and maximum independent variable
values. Appears as the NRNGfields in the Plot Setup input
form.
From Plot Setup, enter values for NRNG.
or
In a program, type
n1 ꢂNmin
n2 ꢂNmax
where n2 > n1
Recenter
All Aplets
Recenters at the crosshairs locations when zooming.
From Plot-Zoom-Set Factors, check (or uncheck)
Recenter
or
In a program, type
1 ꢂ Recenter— to turn recenter on (default).
0 ꢂ Recenter—to turn recenter off.
Root
Function
Contains the last value found by the Root function in the
Plot-FCN menu.
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S1mark–S5mark
Statistics
Sets the mark to use for scatter plots.
From Plot Setup for two-variable statistics, S1mark-
S5mark, then choose a mark.
or
In a program, type
n ꢂ S1mark
where n is 1,2,3,...5
SeqPlot
Sequence
Enables you to choose types of sequence plot: Stairstep
or Cobweb.
From Plot Setup, select SeqPlot, then choose
Stairstepor Cobweb.
or
In a program, type
1 ꢂSeqPlot—for Stairstep.
2 ꢂSeqPlot—for Cobweb.
Simult
Enables you to choose between simultaneous and
sequential graphing of all selected expressions.
Function
Parametric
Polar
From Plot Setup, check (or uncheck) _SIMULT
or
Sequence
In a program, type
1 ꢂ Simult—for simultaneous graphing (default).
0 ꢂ Simult—for sequential graphing.
Slope
Function
Contains the last value found by the Slope function in the
Plot-FCN menu.
StatPlot
Statistics
Enables you to choose types of 1-variable statistics plot
between Histogram or Box-and-Whisker.
From Plot Setup, select StatPlot, then choose
Histogramor BoxWhisker.
or
In a program, type
1ꢂStatPlot—for Histogram.
2ꢂStatPlot—for Box-and-Whisker.
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Umin/Umax
Polar
Sets the minimum and maximum independent values.
Appears as the URNGfield in the Plot Setup input form.
From the Plot Setup input form, enter values for URNG.
or
In a program, type
n1 ꢂ Umin
n2 ꢂ Umax
where n2 > n1
Ustep
Polar
Sets the step size for an independent variable.
From the Plot Setup input form, enter values for USTEP.
or
In a program, type
n ꢂ Ustep
where n > 0
Tmin / Tmax
Parametric
Sets the minimum and maximum independent variable
values. Appears as the TRNGfield in the Plot Setup input
form.
From Plot Setup, enter values for TRNG.
or
In a program, type
n1 ꢂTmin
n2 ꢂTmax
where n2 > n1
Tracing
Turns the tracing mode on or off in Plot view.
In a program, type
All Aplets
1 ꢂ Tracing—to turn Tracing mode on (default).
0 ꢂ Tracing—to turn Tracing mode off.
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Tstep
Sets the step size for the independent variable.
Parametric
From the Plot Setup input form, enter values for TSTEP.
or
In a program, type
n ꢂ Tstep
where n > 0
Xcross
Sets the horizontal coordinate of the crosshairs. Only
works with TRACEoff.
All Aplets
In a program, type
n ꢂ Xcross
Ycross
Sets the vertical coordinate of the crosshairs. Only works
with TRACEoff.
All Aplets
In a program, type
n ꢂ Ycross
Xtick
All Aplets
Sets the distance between tick marks for the horizontal
axis.
From the Plot Setup input form, enter a value for Xtick.
or
In a program, type
n ꢂ Xtick where n > 0
Ytick
All Aplets
Sets the distance between tick marks for the vertical axis.
From the Plot Setup input form, enter a value for Ytick.
or
In a program, type
n ꢂ Ytick where n > 0
Xmin / Xmax
All Aplets
Sets the minimum and maximum horizontal values of the
plot screen. Appears as the XRNGfields (horizontal
range) in the Plot Setup input form.
From Plot Setup, enter values for XRNG.
or
In a program, type
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n1 ꢂ Xmin
n2 ꢂ Xmax
where n2 > n1
Ymin / Ymax
All Aplets
Sets the minimum and maximum vertical values of the plot
screen. Appears as the YRNGfields (vertical range) in the
Plot Setup input form.
From Plot Setup, enter the values for YRNG.
or
In a program, type
n1 ꢂ Ymin
n2 ꢂ Ymax
where n2 > n1
Xzoom
All Aplets
Sets the horizontal zoom factor.
From Plot-ZOOM-Set Factors, enter the value for XZOOM.
or
In a program, type
n ꢂ XZOOM
where n > 0
The default value is 4.
Yzoom
All Aplets
Sets the vertical zoom factor.
From Plot-ZOOM-Set Factors, enter the value for YZOOM.
or
In a program, type
n ꢂ YZOOM
The default value is 4.
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Symbolic-view variables
Angle
All Aplets
Sets the angle mode.
From Symbolic Setup, choose Degrees, Radians, or
Gradsfor angle measure.
or
In a program, type
1ꢂAngle—for Degrees.
2ꢂAngle—for Radians.
3ꢂAngle—for Grads.
F1...F9, F0
Function
Can contain any expression. Independent variable is X.
Example
'SIN(X)' ꢂ F1(X)
You must put single quotes around an expression to keep
it from being evaluated before it is stored. Use
CHARS to type the single quote mark.
X1, Y1...X9,Y9
X0,Y0
Parametric
Can contain any expression. Independent variable is T.
Example
'SIN(4*T)' ꢂ Y1(T):'2*SIN(6*T)' ꢂ
X1(T)
R1...R9, R0
Polar
Can contain any expression. Independent variable is θ.
Example
'2*SIN(2*θ)' ꢂ R1(θ)
U1...U9, U0
Sequence
Can contain any expression. Independent variable is N.
Example
RECURSE (U,U(N-1)*N,1,2) ꢂ U1(N)
E1...E9, E0
Solve
Can contain any equation or expression. Independent
variable is selected by highlighting it in Numeric View.
Example
'X+Y*X-2=Y' ꢂ E1
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S1fit...S5fit
Statistics
Sets the type of fit to be used by the FIT operation in
drawing the regression line.
From Symbolic Setup view, specify the fit in the field for
S1FIT, S2FIT, etc.
or
In a program, store one of the following constant numbers
or names into a variable S1fit, S2fit, etc.
1 Linear
2 LogFit
3 ExpFit
4 Power
5 QuadFit
6 Cubic
7 Logist
8 ExpFit
9 TrigFit
10 UserDefined
Example
Cubic ꢂ S2fit
or
6 ꢂ S2fit
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Numeric-view variables
The following aplet variables control the Numeric view.
The value of the variable applies to the current aplet only.
C1...C9, C0
Statistics
C0through C9, for columns of data. Can contain lists.
Enter data in the Numeric view
or
In a program, type
LISTꢂCn
where n = 0, 1, 2, 3 ... 9
Digits
All Aplets
Number of decimal places to use for Number format in
the HOME view and for labeling axes in the Plot view.
From the Modes view, enter a value in the second field of
NumberFormat.
or
In a program, type
n ꢂDigits
where 0<n <11
Format
All Aplets
Defines the number display format to use for numeric
format in the HOME view and for labeling axes in the Plot
view.
From the Modes view, choose Standard, Fixed,
Scientific, Engineering,Fraction or Mixed
Fraction in the Number Formatfield.
or
In a program, store the constant number (or its name) into
the variable Format.
1 Standard
2 Fixed
3 Sci
4 Eng
5 Fraction
6 MixFraction
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Note that if Fraction or Mixed Fraction is chosen, the
setting will be ignored when labeling axes in Plot view. A
setting of Scientific will be used instead.
Example
ScientificꢂFormat
or
3 ꢂFormat
NumCol
All Aplets except
Statistics aplet
Sets the column to be highlighted in Numeric view.
In a program, type
n ꢂNumCol
where n can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
NumFont
Function
Parametric
Polar
Sequence
Statistics
Enables you to choose the font size in Numeric view.
Does not appear in the Num Setup input form.
Corresponds to the
key in Numeric view.
In a program, type
0 ꢂNumFontfor small (default).
1 ꢂNumFontfor big.
NumIndep
Function
Parametric
Polar
Specifies the list of independent values to be used by
Build Your Own Table.
In a program, type
LISTꢂNumIndep
Sequence
NumRow
All Aplets except
Statistics aplet
Sets the row to be highlighted in Numeric view.
In a program, type
n ꢂNumRow
where n >0
NumStart
Function
Parametric
Polar
Sets the starting value for a table in Numeric view.
From Num Setup, enter a value for NUMSTART.
or
Sequence
In a program, type
n ꢂNumStart
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NumStep
Function
Parametric
Polar
Sets the step size (increment value) for an independent
variable in Numeric view.
From Num Setup, enter a value for NUMSTEP.
or
Sequence
In a program, type
n ꢂNumStep
where n > 0
NumType
Function
Parametric
Polar
Sets the table format.
From Num Setup, choose Automaticor BuildYour
Own.
or
Sequence
In a program, type
0 ꢂ NumTypefor Build Your Own.
1 ꢂ NumTypefor Automatic (default).
NumZoom
Function
Parametric
Polar
Sets the zoom factor in the Numeric view.
From Num Setup, type in a value for NUMZOOM.
or
Sequence
In a program, type
n ꢂ NumZoom
where n > 0
StatMode
Statistics
Enables you to choose between 1-variable and 2-variable
statistics in the Statistics aplet. Does not appear in the Plot
Setup input form. Corresponds to the
menu keys in Numeric View.
and
In a program, store the constant name (or its number) into
the variable StatMode. 1VAR=1, 2VAR=2.
Example
1VAR ꢂ StatMode
or
1 ꢂ StatMode
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Note variables
The following aplet variable is available in Note view.
NoteText
All Aplets
Use NoteTextto recall text previously entered in Note
view.
Sketch variables
The following aplet variables are available in Sketch
view.
Page
All Aplets
Sets a page in a sketch set. The graphics can be viewed
one at a time using the
and
keys.
The Page variable refers to the currently displayed page
of a sketch set.
In a program, type
graphicname ꢂ Page
PageNum
All Aplets
Sets a number for referring to a particular page of the
sketch set (in Sketch view).
In a program, type the page that is shown when
SKETCH is pressed.
n ꢂ PageNum
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19
Extending aplets
Aplets are the application environments where you
explore different classes of mathematical operations.
You can extend the capability of the HP 39gs in the
following ways:
•
Create new aplets, based on existing aplets, with
specific configurations such as angle measure,
graphical or tabular settings, and annotations.
•
•
•
Transmit aplets between HP 39gs calculators via an
infra red link.
Download e-lessons (teaching aplets) from
Hewlett-Packard’s Calculator web site.
Program new aplets. See chapter 18,
“Programming”, for further details.
Creating new aplets based on existing aplets
You can create a new aplet based on an existing aplet.
To create a new aplet, save an existing aplet under a new
name, then modify the aplet to add the configurations
and the functionality that you want.
Information that defines an aplet is saved automatically
as it is entered into the calculator.
To keep as much memory available for storage as
possible, delete any aplets you no longer need.
Example
This example demonstrates how to create a new aplet by
saving a copy of the built-in Solve aplet. The new aplet is
saved under the name “TRIANGLES” contains the
formulas commonly used in calculations involving
right-angled triangles.
Extending aplets
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1. Open the Solve aplet and save it under the new
name.
Solve
|
T R I A N G L E S
2. Enter the four formulas:
θ
O
H
θ
A
H
θ
O
A
A
B
C
3. Decide whether you want the aplet to operate in
Degrees, Radians, or Grads.
MODES
Degrees
4. View the Aplet Library. The “TRIANGLES” aplet is
listed in the Aplet Library.
The Solve aplet can now
be reset and used for
other problems.
19-2
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Using a customized aplet
To use the “Triangles” aplet, simply select the appropriate
formula, change to the Numeric view and solve for the
missing variable.
Find the length of a ladder leaning against a vertical wall
o
if it forms an angle of 35 with the horizontal and
extends 5 metres up the wall.
1. Select the aplet.
TRIANGLES
2. Choose the sine formula
in E1.
3. Change to the Numeric
view and enter the
known values.
35
5
4. Solve for the missing
value.
The length of the ladder
is approximately 8.72 metres
Resetting an aplet
Resetting an aplet clears all data and resets all default
settings.
To reset an aplet, open the Library, select the aplet and
press
.
You can only reset an aplet that is based on a built-in
aplet if the programmer who created it has provided a
Reset option.
Extending aplets
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19-3
Annotating an aplet with notes
The Note view (
NOTE) attaches a note to the current
aplet. See Chapter 17, “Notes and sketches”.
Annotating an aplet with sketches
The Sketch view (
SKETCH) attaches a picture to the
current aplet. See chapter 17, “Notes and sketches”.
H I N T
Notes and sketches that you attach to an aplet become
part of the aplet. When you transfer the aplet to another
calculator, the associated note and sketch are transferred
as well.
Downloading e-lessons from the web
In addition to the standard aplets that come with the
calculator, you can download aplets from the world wide
web. For example, Hewlett-Packard’s Calculators web
site contains aplets that demonstrate certain mathematical
concepts. Note that you need the Graphing Calculator
Connectivity Kit in order to load aplets from a PC.
Hewlett-Packard’s Calculators web site can be found at:
http://www.hp.com/calculators
Sending and receiving aplets
A convenient way to distribute or share problems in class
and to turn in homework is to transmit (copy) aplets
directly from one HP 39gs to another. This can take place
via the infrared port or via a suitable cable. (You can use
a serial cable with a 4-pin mini-USB connector, which
plugs into the RS232 port on the calculator. The serial
cable is available as a separate accessory.)
You can also send aplets to, and receive aplets from, a
PC. This requires special software running on the PC (such
as the PC Connectivity Kit). A USB cable with a 5-pin mini-
USB connector is provided with the hp39gs for
connecting with a PC. It plugs into the USB port on the
calculator.
19-4
Extending aplets
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To transmit
an aplet
1. Connect the PC or aplet disk drive to the calculator by
cable
or
align the two calculators’ infrared ports by matching
up the triangle marks on the rims of the calculators.
Place the calculators no more than 4 inches (10 cm)
apart.
2. Sending calculator: Open the Library, highlight the
aplet to send, and press
.
–
The SEND TO menu appears with the following
options:
HP39G (IRDA) = to send via high-speed infrared
HP39/40 (USB) = to send via the USB port
HP39/40 (SER) = to send via the RS232 serial port
USB DISK DRIVE = to send to a disk drive via the USB
port
SER. DISK DRIVE = to send to a disk drive via the
RS232 serial port
Note: choose a disk drive option if you are using
the hp39gs connectivity kit to transfer the aplet.
Highlight your selection and press
.
–
If transmitting to a disk drive, you have the
options of sending to the current (default)
directory or to another directory.
3. Receiving calculator: Open the aplet library and
press
.
–
The RECEIVE FROM menu appears with the following
options:
HP39G (IRDA) = to receive via high-speed infrared
HP39G = to receive via low-speed infrared
HP39/40 (USB) = to receive via the USB port
HP39/40 (SER) = to receive via the RS232 serial port
USB DISK DRIVE = to receive from a disk drive via the
USB port
SER. DISK DRIVE = to receive from a disk drive via the
RS232 serial port
Extending aplets
19-5
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Note: choose a disk drive option if you are using
the hp39gs connectivity kit to transfer the aplet.
Highlight your selection and press
.
The Transmit annunciator— —is displayed until
transmission is complete.
If you are using the PC Connectivity Kit to download
aplets from a PC, you will see a list of aplets in the PC’s
current directory. Check as many items as you would like
to receive.
Sorting items in the aplet library menu list
Once you have entered information into an aplet, you
have defined a new version of an aplet. The information
is automatically saved under the current aplet name, such
as “Function.” To create additional aplets of the same
type, you must give the current aplet a new name.
The advantage of storing an aplet is to allow you to keep
a copy of a working environment for later use.
The aplet library is where you go to manage your aplets.
Press
. Highlight (using the arrow keys) the name
of the aplet you want to act on.
To sort the
aplet list
In the aplet library, press
. Select the sorting scheme
and press
.
• Chronologicallyproduces a chronological order
based on the date an aplet was last used. (The last-
used aplet appears first, and so on.)
• Alphabeticallyproduces an alphabetical order
by aplet name.
To delete an
aplet
You cannot delete a built-in aplet. You can only clear its
data and reset its default settings.
To delete a customized aplet, open the aplet library,
highlight the aplet to be deleted, and press
. To
delete all custom aplets, press
CLEAR.
19-6
Extending aplets
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R
Reference information
Glossary
aplet
A small application, limited to one
topic. The built-in aplet types are
Function, Parametric, Polar,
Sequence, Solve, Statistics,
Inference, Finance, Trig Explorer,
Quad Explorer, Linear Solver and
Triangle Solve. An aplet can be filled
with the data and solutions for a
specific problem. It is reusable (like a
program, but easier to use) and it
records all your settings and
definitions.
command
An operation for use in programs.
Commands can store results in
variables, but do not display results.
Arguments are separated by semi-
colons, such as DISP
expression;line#.
expression
function
A number, variable, or algebraic
expression (numbers plus functions)
that produces a value.
An operation, possibly with
arguments, that returns a result. It
does not store results in variables. The
arguments must be enclosed in
parentheses and separated with
commas (or periods in Comma
mode), such as
CROSS(matrix1,matrix2).
HOME
Library
The basic starting point of the
calculator. Go to HOME to do
calculations.
For aplet management: to start, save,
reset, send and receive aplets.
R-1
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list
A set of values separated by commas
(periods if the Decimal Mark mode is
set to Comma) and enclosed in
braces. Lists are commonly used to
enter statistical data and to evaluate
a function with multiple values.
Created and manipulated by the List
editor and catalog.
matrix
A two-dimensional array of values
separated by commas (periods if the
Decimal Mark mode is set to Comma)
and enclosed in nested brackets.
Created and manipulated by the
Matrix catalog and editor. Vectors
are also handled by the Matrix
catalog and editor.
menu
A choice of options given in the
display. It can appear as a list or as
a set of menu-key labels across the
bottom of the display.
menu keys
The top row of keys. Their operations
depend on the current context. The
labels along the bottom of the display
show the current meanings.
note
Text that you write in the Notepad or
in the Note view for a specific aplet.
program
sketch
A reusable set of instructions that you
record using the Program editor.
A drawing that you make in the
Sketch view for a specific aplet.
variable
The name of a number, list, matrix,
note, or graphic that is stored in
memory. Use
to retrieve.
to store and use
vector
A one-dimensional array of values
separated by commas (periods if the
Decimal Mark mode is set to Comma)
and enclosed in single brackets.
Created and manipulated by the
Matrix catalog and editor.
R-2
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views
The possible contexts for an aplet:
Plot, Plot Setup, Numeric, Numeric
Setup, Symbolic, Symbolic Setup,
Sketch, Note, and special views like
split screens.
Resetting the HP 39gs
If the calculator “locks up” and seems to be stuck, you
must reset it. This is much like resetting a PC. It cancels
certain operations, restores certain conditions, and clears
temporary memory locations. However, it does not clear
stored data (variables, aplet databases, programs) unless
you use the procedure, “To erase all memory and reset
defaults”.
To reset using
the keyboard
Press and hold the
key and the third menu key
simultaneously, then release them.
If the calculator does not respond to the above key
sequence, then:
1. Turn the calculator over and locate the small hole in
the back of the calculator.
2. Insert the end of a straightened metal paper clip into
the hole as far as it will go. Hold it there for 1
second, then remove it.
3. Press
If necessary, press
and the first and
last menu keys simultaneously. (Note: This will erase
your calculator memory.)
To erase all memory and reset defaults
If the calculator does not respond to the above resetting
procedures, you might need to restart it by erasing all of
memory. You will lose everything you have stored. All
factory-default settings are restored.
1. Press and hold the
key, the first menu key, and
the last menu key simultaneously.
2. Release all keys in the reverse order.
Note: To cancel this process, release only the top-row
keys, then press the third menu key.
R-3
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If the calculator does not turn on
If the HP 39gs does not turn on follow the steps below
until the calculator turns on. You may find that the
calculator turns on before you have completed the
procedure. If the calculator still does not turn on, please
contact Customer Support for further information.
1. Press and hold the
2. Press and hold the
key for 10 seconds.
key and the third menu key
simultaneously. Release the third menu key, then
release the key.
3. Press and hold the
key, the first menu key, and
the sixth menu key simultaneously. Release the sixth
menu key, then release the first menu key, and then
release the
key.
4. Locate the small hole in the back of the calculator.
Insert the end of a straightened metal paper clip into
the hole as far as it will go. Hold it there for 1
second, then remove it. Press the
5. Remove the batteries (see “Batteries” on page R-4),
press and hold the key for 10 seconds, and
then put the batteries back in. Press the key.
key.
Operating details
Operating temperature: 0° to 45°C (32° to 113°F).
Storage temperature: –20° to 65°C (–4° to 149°F).
Operating and storage humidity: 90% relative
humidity at 40°C (104°F) maximum. Avoid getting the
calculator wet.
Battery operates at 6.0V dc, 80mA maximum.
Batteries
The calculator uses 4 AAA(LR03) batteries as main power
and a CR2032 lithium battery for memory backup.
Before using the calculator, please install the batteries
according to the following procedure.
R-4
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To install the main
batteries
a. Slide up the battery compartment cover as illustrated.
b. Insert 4 new AAA (LR03) batteries into the main
compartment. Make sure each battery is inserted in the
indicated direction.
To install the
backup battery
a. Press down the holder. Push the plate to the shown
direction and lift it.
b. Insert a new CR2032 lithium battery. Make sure its
positive (+) side is facing up.
c. Replace the plate and push it to the original place.
After installing the batteries, press
on.
to turn the power
Warning: It is recommended that you replace this battery
every 5 years. When the low battery icon is displayed,
you need to replace the batteries as soon as possible.
However, avoid removing the backup battery and main
batteries at the same time to avoid data lost.
R-5
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Variables
Home variables
The home variables are:
Category
Complex
Graphic
Library
Available name
Z1...Z9, Z0
G1...G9, G0
Function
Parametric
Polar
Sequence
Solve
Statistics
User-named
List
L1...L9, L0
M1...M9, M0
Matrix
Modes
Ans
Date
HAngle
HDigits
HFormat
Ierr
Time
Notepad
Program
User-named
Editline
User-named
Real
A...Z, θ
R-6
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Function aplet variables
The function aplet variables are:
Category
Available name
Plot
Axes
Xcross
Ycross
Xtick
Ytick
Xmin
Connect
Coord
FastRes
Grid
Indep
InvCross
Labels
Recenter
Simult
Tracing
Xmax
Ymin
Ymax
Xzoom
Yxoom
Plot-FCN
Symbolic
Area
Root
Extremum
Isect
Slope
Angle
F1
F6
F7
F8
F9
F0
F2
F3
F4
F5
Numeric
Digits
NumRow
Format
NumStart
NumStep
NumType
NumZoom
NumCol
NumFont
NumIndep
Note
NoteText
Page
Sketch
PageNum
R-7
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Parametric aplet variables
The parametric aplet variables are:
Category
Available name
Plot
Axes
Tracing
Tstep
Xcross
Ycross
Xtick
Ytick
Xmin
Connect
Coord
Grid
Indep
InvCross
Labels
Recenter
Simult
Tmin
Xmax
Ymin
Ymax
Xzoom
Yzoom
Tmax
Symbolic
Angle
X1
Y5
X6
Y6
X7
Y7
X8
Y8
X9
Y9
X0
Y0
Y1
X2
Y2
X3
Y3
X4
Y4
X5
Numeric
Digits
NumRow
Format
NumStart
NumStep
NumType
NumZoom
NumCol
NumFont
NumIndep
Note
NoteText
Page
Sketch
PageNum
R-8
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Polar aplet variables
The polar aplet variables are:
Category
Available names
Plot
Axes
Connect
Coord
Xcross
Ycross
Xtick
Ytick
Xmin
Grid
Indep
InvCross
Labels
Recenter
Simult
Umin
Xmax
Ymin
Ymax
Xzoom
Yxoom
Umax
θstep
Tracing
Symbolic
Numeric
Angle
R1
R6
R7
R8
R9
R0
R2
R3
R4
R5
Digits
NumRow
Format
NumStart
NumStep
NumType
NumZoom
NumCol
NumFont
NumIndep
Note
NoteText
Page
Sketch
PageNum
R-9
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Sequence aplet variables
The sequence aplet variables are:
Category
Available name
Plot
Axes
Coord
Grid
Indep
InvCross
Labels
Nmin
Tracing
Xcross
Ycross
Xtick
Ytick
Xmin
Xmax
Nmax
Ymin
Recenter
SeqPlot
Simult
Ymax
Xzoom
Yzoom
Symbolic
Numeric
Angle
U1
U2
U3
U4
U6
U7
U8
U9
U0
U5
Digits
Format
NumCol
NumFont
NumIndep
NumRow
NumStart
NumStep
NumType
NumZoom
Note
NoteText
Page
Sketch
PageNum
R-10
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Solve aplet variables
The solve aplet variables are:
Category
Available name
Plot
Axes
Connect
Coord
FastRes
Grid
Xcross
Ycross
Xtick
Ytick
Xmin
Indep
Xmax
InvCross
Labels
Recenter
Tracing
Ymin
Ymax
Xzoom
Yxoom
Symbolic
Numeric
Angle
E1
E2
E3
E4
E6
E7
E8
E9
E0
E5
Digits
Format
NumCol
NumRow
Note
NoteText
Page
Sketch
PageNum
R-11
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Statistics aplet variables
The statistics aplet variables are:
Category
Available name
Plot
Axes
S4mark
S5mark
StatPlot
Tracing
Xcross
Ycross
Xtick
Ytick
Xmin
Connect
Coord
Grid
Hmin
Hmax
Hwidth
Indep
InvCross
Labels
Recenter
S1mark
S2mark
S3mark
Xmax
Ymin
Ymax
Xzoom
Yxoom
Symbolic
Numeric
Angle
S1fit
S2fit
S3fit
S4fit
S5fit
C0,...C9
Digits
Format
NumCol
NumFont
NumRow
StatMode
Stat-One
Stat-Two
MaxΣ
MeanΣ
Median
MinΣ
NΣ
Q3
PSDev
SSDev
PVarΣ
SVarΣ
TotΣ
Q1
Corr
Cov
Fit
MeanX
MeanY
RelErr
ΣX
ΣX2
ΣXY
ΣY
ΣY2
Note
NoteText
Page
Sketch
PageNum
R-12
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MATH menu categories
Math functions
The math functions are:
Category
Available name
Calculus
∂
∫
TAYLOR
Complex
Constant
ARG
IM
RE
CONJ
e
i
MAXREAL
MINREAL
π
Hyperb.
ACOSH
ASINH
ATANH
COSH
TANH
ALOG
EXP
EXPM1
LNP1
SINH
List
CONCAT
ΔLIST
MAKELIST
πLIST
POS
REVERSE
SIZE
ΣLIST
SORT
Loop
ITERATE
RECURSE
Σ
R-13
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Category
Available name (Continued)
Matrix
COLNORM
COND
QR
RANK
CROSS
DET
ROWNORM
RREF
DOT
SCHUR
SIZE
SPECNORM
SPECRAD
SVD
EIGENVAL
EIGENVV
IDENMAT
INVERSE
LQ
SVL
LSQ
LU
TRACE
TRN
MAKEMAT
Polynom.
Prob.
POLYCOEF
POLYEVAL
POLYFORM
POLYROOT
COMB
!
PERM
RANDOM
UTPC
UTPF
UTPN
UTPT
Real
CEILING
DEG→RAD
FLOOR
FNROOT
FRAC
HMS→
→HMS
INT
MIN
MOD
%
%CHANGE
%TOTAL
RAD→DEG
ROUND
SIGN
MANT
MAX
TRUNCATE
XPON
Stat-Two
Symbolic
PREDX
PREDY
=
QUAD
QUOTE
|
ISOLATE
LINEAR?
R-14
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Category
Available name (Continued)
Tests
AND
<
≤
= =
≠
IFTE
NOT
OR
XOR
>
≥
Trig
ACOT
ACSC
ASEC
COT
CSC
SEC
Program constants
The program constants are:
Category
Available name
Angle
Degrees
Grads
Radians
Format
Standard
Fixed
Sci
Eng
Fraction
SeqPlot
S1...5fit
Cobweb
Stairstep
Linear
LogFit
ExpFit
Power
QuadFit
Cubic
Logist
User
Trigonometric Exponent
StatMode
StatPlot
Stat1Var
Stat2Var
Hist
BoxW
R-15
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Physical Constants
The physical constants are:
Category
Available Name
Chemist
• Avogadro(Avogadro’s Number,
NA)
• Boltz. (Boltmann, k)
• mol. vo... (molar volume, Vm)
• univ gas(universal gas, R)
• std temp(standard temperature,
St dT)
• std pres(standard pressure,
St dP)
Phyics
• StefBolt(Stefan-Boltzmann, σ)
•
light s...(speed of light, c)
• permitti(permittivity, ε0)
• permeab(permeability, μ0)
• acce gr... (acceleration of
gravity, g)
• gravita...(gravitation, G)
Quantum
• Plank’s(Plank’s constant, h)
• Dirac’s(Dirac’s, hbar)
• e charge(electronic charge, q)
• e mass(electron mass, me)
• q/me ra...(q/me ratio, qme)
• proton m(proton mass, mp)
• mp/me r...(mp/me ratio,
mpme)
• fine str(fine structure, α)
• mag flux(magnetic flux, φ)
• Faraday(Faraday, F)
• Rydberg(Rydberg, R∞ )
• Bohr rad (Bohr radius, a0)
• Bohr mag(Bohr magneton, μB)
• nuc. mag (nuclear magneton,
μN)
• photon...(photon wavelength,
λ)
• photon...(photon frequency,
f0)
• Compt w...(Compton
wavelength, λc)
R-16
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Program commands
The program commands are:
Category
Command
Aplet
CHECK
SELECT
SETVIEWS
UNCHECK
Branch
Drawing
Graphic
IF
CASE
IFERR
RUN
THEN
ELSE
END
STOP
ARC
BOX
ERASE
FREEZE
LINE
PIXOFF
PIXON
TLINE
DISPLAY→
→DISPLAY
→GROB
MAKEGROB
PLOT→
→PLOT
GROBNOT
GROBOR
REPLACE
SUB
GROBXOR
ZEROGROB
Loop
FOR
=
UNTIL
END
TO
WHILE
REPEAT
END
STEP
END
DO
BREAK
Matrix
ADDCOL
ADDROW
DELCOL
DELROW
EDITMAT
RANDMAT
REDIM
REPLACE
SCALE
SCALEADD
SUB
SWAPCOL
SWAPROW
Print
PRDISPLAY
PRHISTORY
PRVAR
Prompt
BEEP
FREEZE
GETKEY
INPUT
MSGBOX
PROMPT
WAIT
CHOOSE
CLRVAR
DISP
DISPXY
DISPTIME
EDITMAT
Stat-One
DO1VSTATS
RANDSEED
SETFREQ
SETSAMPLE
R-17
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Category
Command (Continued)
Stat-Two
DO2VSTATS
SETDEPEND
SETINDEP
Status messages
Message
Meaning
Bad Argument
Type
Incorrect input for this
operation.
Bad Argument
Value
The value is out of range for this
operation.
Infinite Result
Math exception, such as 1/0.
Insufficient
Memory
You must recover some memory
to continue operation. Delete
one or more matrices, lists,
notes, or programs (using
catalogs), or custom (not built-
in) aplets (using
MEMORY).
Insufficient
Statistics Data
Not enough data points for the
calculation. For two-variable
statistics there must be two
columns of data, and each
column must have at least four
numbers.
Invalid Dimension
Array argument had wrong
dimensions.
Invalid Statistics
Data
Need two columns with equal
numbers of data values.
R-18
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Message
Meaning (Continued)
Invalid Syntax
The function or command you
entered does not include the
proper arguments or order of
arguments. The delimiters
(parentheses, commas,
periods, and semi-colons) must
also be correct. Look up the
function name in the index to
find its proper syntax.
Name Conflict
The | (where) function
attempted to assign a value to
the variable of integration or
summation index.
No Equations
Checked
You must enter and check an
equation (Symbolic view)
before evaluating this function.
(OFF SCREEN)
Receive Error
Function value, root, extremum,
or intersection is not visible in
the current screen.
Problem with data reception
from another calculator. Re-
send the data.
Too Few
Arguments
The command requires more
arguments than you supplied.
Undefined Name
Undefined Result
The global variable named
does not exist.
The calculation has a
mathematicallyundefinedresult
(such as 0/0).
Out of Memory
You must recover a lot of
memory to continue operation.
Delete one or more matrices,
lists, notes, or programs (using
catalogs), or custom (not built-
in) aplets (using
MEMORY).
R-19
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Limited Warranty
HP 39gs Graphing Calculator; Warranty period: 12
months
1. HP warrants to you, the end-user customer, that HP
hardware, accessories and supplies will be free from
defects in materials and workmanship after the date
of purchase, for the period specified above. If HP
receives notice of such defects during the warranty
period, HP will, at its option, either repair or replace
products which prove to be defective. Replacement
products may be either new or like-new.
2. HP warrants to you that HP software will not fail to
execute its programming instructions after the date of
purchase, for the period specified above, due to
defects in material and workmanship when properly
installed and used. If HP receives notice of such
defects during the warranty period, HP will replace
software media which does not execute its
programming instructions due to such defects.
3. HP does not warrant that the operation of HP
products will be uninterrupted or error free. If HP is
unable, within a reasonable time, to repair or replace
any product to a condition as warranted, you will be
entitled to a refund of the purchase price upon
prompt return of the product with proof of purchase.
4. HP products may contain remanufactured parts
equivalent to new in performance or may have been
subject to incidental use.
5. Warranty does not apply to defects resulting from (a)
improper or inadequate maintenance or calibration,
(b) software, interfacing, parts or supplies not
supplied by HP, (c) unauthorized modification or
misuse, (d) operation outside of the published
environmental specifications for the product, or (e)
improper site preparation or maintenance.
W-1
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6. HP MAKES NO OTHER EXPRESS WARRANTY OR
CONDITION WHETHER WRITTEN OR ORAL. TO
THE EXTENT ALLOWED BY LOCAL LAW, ANY
IMPLIED WARRANTY OR CONDITION OF
MERCHANTABILITY, SATISFACTORY QUALITY, OR
FITNESS FOR A PARTICULAR PURPOSE IS LIMITED
TO THE DURATION OF THE EXPRESS WARRANTY
SET FORTH ABOVE. Some countries, states or
provinces do not allow limitations on the duration of
an implied warranty, so the above limitation or
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you specific legal rights and you might also have
other rights that vary from country to country, state to
state, or province to province.
7. TO THE EXTENT ALLOWED BY LOCAL LAW, THE
REMEDIES IN THIS WARRANTY STATEMENT ARE
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SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR
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DAMAGE, WHETHER BASED IN CONTRACT, TORT,
OR OTHERWISE. Some countries, States or provinces
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or consequential damages, so the above limitation or
exclusion may not apply to you.
8. The only warranties for HP products and services are
set forth in the express warranty statements
accompanying such products and services. HP shall
not be liable for technical or editorial errors or
omissions contained herein.
FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND
NEW ZEALAND: THE WARRANTY TERMS CONTAINED
IN THIS STATEMENT, EXCEPT TO THE EXTENT
LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT
OR MODIFY AND ARE IN ADDITION TO THE
MANDATORY STATUTORY RIGHTS APPLICABLE TO THE
SALE OF THIS PRODUCT TO YOU.
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Service
Europe
Country :
Austria
Telephone numbers
+43-1-3602771203
+32-2-7126219
Belgium
Denmark
+45-8-2332844
Eastern Europe +420-5-41422523
countries
Finland
France
+35-89640009
+33-1-49939006
+49-69-95307103
+420-5-41422523
+31-2-06545301
+39-02-75419782
+47-63849309
Germany
Greece
Holland
Italy
Norway
Portugal
Spain
+351-229570200
+34-915-642095
+46-851992065
Sweden
Switzerland
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(German)
+41-22-8278780
(French)
+39-02-75419782
(Italian)
Turkey
UK
+420-5-41422523
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Czech Republic +420-5-41422523
South Africa
Luxembourg
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+32-2-7126219
Other European +420-5-41422523
countries
Asia Pacific Country :
Australia
Telephone numbers
+61-3-9841-5211
+61-3-9841-5211
Singapore
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L.America Country:
Argentina
Telephone numbers
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Brazil
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Telephone numbers
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Canada
(905) 206-4663 or
800- HP INVENT
ROTC = Rest of the country
Please logon to http://www.hp.com for the latest service
and support information.h
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Regulatory information
Federal
Communications
Commission Notice
This equipment has been tested and found to comply with
the limits for a Class B digital device, pursuant to Part 15
of the FCC Rules. These limits are designed to provide
reasonable protection against harmful interference in a
residential installation. This equipment generates, uses,
and can radiate radio frequency energy and, if not
installed and used in accordance with the instructions,
may cause harmful interference to radio communications.
However, there is no guarantee that interference will not
occur in a particular installation. If this equipment does
cause harmful interference to radio or television
reception, which can be determined by turning the
equipment off and on, the user is encouraged to try to
correct the interference by one or more of the following
measures:
•
•
Reorient or relocate the receiving antenna.
Increase the separation between the equipment and
the receiver.
•
•
Connect the equipment into an outlet on a circuit
different from that to which the receiver is connected.
Consult the dealer or an experienced radio or
television technician for help.
Modifications
Cables
The FCC requires the user to be notified that any changes
or modifications made to this device that are not
expressly approved by Hewlett-Packard Company may
void the user's authority to operate the equipment.
Connections to this device must be made with shielded
cables with metallic RFI/EMI connector hoods to maintain
compliance with FCC rules and regulations.
Declaration of
This device complies with Part 15 of the FCC Rules.
Operation is subject to the following two conditions: (1)
this device may not cause harmful interference, and (2)
this device must accept any interference received,
including interference that may cause undesired
operation.
Conformity for
Products Marked
with FCC Logo,
United States Only
For questions regarding your product, contact:
Hewlett-Packard Company
P. O. Box 692000, Mail Stop 530113
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Houston, Texas 77269-2000
Or, call
1-800-474-6836
For questions regarding this FCC declaration, contact:
Hewlett-Packard Company
P. O. Box 692000, Mail Stop 510101
Houston, Texas 77269-2000
Or, call
1-281-514-3333
To identify this product, refer to the part, series, or model
number found on the product.
Canadian Notice
Avis Canadien
This Class B digital apparatus meets all requirements of
the Canadian Interference-Causing Equipment
Regulations.
Cet appareil numérique de la classe B respecte toutes les
exigences du Règlement sur le matériel brouilleur du
Canada.
European Union
Regulatory Notice
This product complies with the following EU Directives:
•
•
Low Voltage Directive 73/23/EEC
EMC Directive 89/336/EEC
Compliance with these directives implies conformity to
applicable harmonized European standards (European
Norms) which are listed on the EU Declaration of
Conformity issued by Hewlett-Packard for this product or
product family.
This compliance is indicated by the following conformity
marking placed on the product:
xxxx*
This marking is valid for EU
non-harmonized Telecom products.
*Notified body number (used only if
applicable - refer to the product label)
This marking is valid for non-Tele-
com prodcts and EU harmonized
Telecom products (e.g. Bluetooth).
Japanese Notice
この装置は、 情報処理装置等電波障害自主規制協議会
（VCCI） の基準に基づ く ク ラ ス B 情報技術装置です。 この装
置は、 家庭環境で使用する こ と を目的と し ていますが、 この
装置がラジオやテレビジ ョ ン受信機に近接し て使用される と、
受信障害を引き起こすこ とがあ り ます。
取り扱い説明書に従って正しい取り扱いを し て く だ さい。
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Korean Notice
Disposal of Waste
Equipment by Users
in Private
Household in the
European Union
This symbol on the product or on its
packaging indicates that this product
must not be disposed of with your other
household waste. Instead, it is your
responsibility to dispose of your waste
equipment by handing it over to a
designated collection point for the
recycling of waste electrical and
electronic equipment. The separate collection and
recycling of your waste equipment at the time of disposal
will help to conserve natural resources and ensure that it
is recycled in a manner that protects human health and
the environment. For more information about where you
can drop off your waste equipment for recycling, please
contact your local city office, your household waste
disposal service or the shop where you purchased the
product.
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Index
A
absolute value 13-5
add 13-3
algebraic entry 1-19
alpha characters
typing 1-6
alphabetical sorting 19-6
angle measure 1-10
in statistics 10-12
setting 1-11
animation 17-5
creating 17-5
annunciators 1-3
Ans (last answer) 1-24
antilogarithm 13-4, 13-9
aplet
canceling operations in 1-1
Numeric view 1-17
Symbolic view 1-16
a note to an aplet 17-1
a sketch to an aplet 17-3
attaching notes 19-4
clearing 19-3
copying 19-4
definition of R-1
deleting 19-6
Function 13-21
Inference 11-1
key 1-4
library 19-6
Linear Solver 8-1
opening 1-16
Parametric 4-1
Polar 5-1
receiving 19-5
resetting 19-3
sending 19-4, 19-5
Sketch view 17-1
Solve 7-1
B
bad argument R-18
bad guesses error message 7-7
batteries R-4
sorting 19-6
statistics 10-1
transmitting 19-5
Triangle Solver 9-1
aplet commands
CHECK 18-14
SELECT 18-14
SETVIEWS 18-17
UNCHECK 18-17
aplet variables
box-and-whisker plot 10-16
branch commands
CASE...END 18-18
IF...THEN...ELSE...END 18-18
IFERR...THEN...ELSE 18-18
branch structures 18-17
build your own table 2-19
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C
calculus
operations 13-7
catalogs 1-30
i 13-8
chronological sorting 19-6
circle drawing 17-4
clearing
maximum real number 13-8
minimum real number 13-8
contrast
aplet 19-3
characters 1-22
display 1-22
decreasing display 1-2
display history 1-25
edit line 1-22
lists 16-6
plot 2-7
cobweb graph 6-1
coefficients
polynomial 13-11
columns
changing position 18-25
combinations 13-12
commands
aplet 18-14
branch 18-17
definition of R-1
drawing 18-19
graphic 18-21
loop 18-23
inverse hyperbolic 13-9
print 18-26
program 18-4, R-17
stat-one 18-30
stat-two 18-30
with matrices 15-10
complex number functions 13-5,
13-16
matrices 15-3
notes in Notepad 17-6
conjugate 13-7
imaginary part 13-7
real part 13-7
complex numbers 1-29
entering 1-29
vector 15-11
curve fitting 10-12, 10-17
math functions 13-7
storing 1-29
confidence intervals 11-15
conjugate 13-7
connecting
D
data set definition 10-8
date, setting 18-28
data points 10-19
variable 18-32
via infrared 19-5
via serial cable 19-5
via USB cable 19-5
debugging programs 18-7
decimal
changing format 1-10
scaling 2-14, 2-15
decreasing display contrast 1-2
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definite integral 13-6
deleting
aplet 19-6
lists 16-6
matrices 15-5
programs 18-9
statistical data 10-11
delimiters, programming 18-1
derivatives
definition of 13-6
in Function aplet 13-22
in Home 13-21
determinant
Program catalog 18-2
square matrix 15-11
differentiation 13-6
display 18-21
adjusting contrast 1-2
annunciator line 1-2
capture 18-21
clearing 1-2
engineering number format 1-11
date and time 18-28
element 15-5
solving 7-1
erasing a line in Sketch view 18-20
constant? 7-7
elements 16-4
engineering 1-10
fixed 1-10
fraction 1-10
history 1-22
line 1-23
matrices 15-5
parts of 1-2
fit 10-13
printing contents 18-26
rescaling 2-13
scientific 1-10
scrolling through history 1-25
soft key labels 1-2
standard 1-10
divide 13-3
entering in HOME 1-19
drawing
circles 17-4
keys 17-4
plot 3-3
extremum 3-10
lines and boxes 17-3
drawing commands
ARC 18-19
F
factorial 13-12
BOX 18-20
FastRes variable 18-32
fit
ERASE 18-20
FREEZE 18-20
LINE 18-20
a curve to 2VAR data 10-17
choosing 10-12
PIXOFF 18-20
PIXON 18-20
defining your own 10-13
fixed number format 1-10
TLINE 18-20
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font size
split-screen view 2-14
splitting into plot and close-up
change 3-8, 17-5
forecasting 10-20
fraction number format 1-11
full-precision display 1-10
function
splitting into plot and table 2-13
statistical data 10-15
analyze graph with FCN tools 3-4
definition 2-2, R-1
entering 1-19
gamma 13-12
intersection point 3-5
math menu R-13
slope 3-5
syntax 13-2
tracing 2-8
two-variable statistics 10-18
GROBXOR 18-22
Function aplet 2-20, 3-1
function variables
area 18-32
REPLACE 18-22
axes 18-32
SUB 18-22
connect 18-32
fastres 18-32
ZEROGROB 18-23
graphics
grid 18-33
copying 17-6
in menu map R-7
indep 18-33
isect 18-34
labels 18-34
Recenter 18-34
root 18-34
range 10-18
ycross 18-37
G
glossary R-1
graph
analyzing statistical data in 10-19
auto scale 2-14
box-and-whisker 10-16
capture current display 18-21
cobweb 6-1
evaluating expressions 2-4
reusing lines 1-23
variables 14-1, 14-7, R-6
horizontal zoom 18-38
hyperbolic
comparing 2-5
connected points 10-17
defining the independent variable
18-36
maths functions 13-10
hyperbolic trigonometry
ACOSH 13-9
drawing axes 2-7
expressions 3-3
grid points 2-7
ALOG 13-9
histogram 10-15
ASINH 13-9
in Solve aplet 7-7
one-variable statistics 10-18
overlaying 2-15
ATANH 13-9
COSH 13-9
EXP 13-10
scatter 10-15, 10-17
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EXPM1 13-10
LNP1 13-10
SINH 13-9
intermediate guesses 7-7
TANH 13-9
hypothesis
alternative 11-2
inference tests 11-8
null 11-2
statistics data R-18
syntax R-19
inverse hyperbolic functions 13-10
inverting matrices 15-8
tests 11-2
I
i 13-8
implied multiplication 1-20
importing
graphics 17-6
notes 17-8
increasing display contrast 1-2
indefinite integral
using symbolic variables 13-23
independent values
adding to table 2-18
independent variable
defined for Tracing mode 18-33
inference
keyboard
entry keys 1-5
math functions 1-7
Notepad keys 17-8
confidence intervals 11-15
hypothesis tests 11-8
One-Proportion Z-Interval 11-17
One-Sample Z-Interval 11-15
One-Sample Z-Test 11-8
Two-Proportion Z-Interval 11-17
Two-Proportion Z-Test 11-11
Two-Sample T-Interval 11-19
Two-Sample Z-Interval 11-16
infinite result R-18
L
labeling
parts of a sketch 17-5
library, managing aplets in 19-6
list
infrared
arithmetic with 16-7
calculate sequence of elements
transmission of aplets 19-5
initial guess 7-5
input forms
calculating product of 16-8
composed from differences 16-7
concatenating 16-7
counting elements in 16-9
creating 16-1, 16-3, 16-4, 16-5
deleting 16-6
resetting default values 1-9
setting Modes 1-11
insufficient memory R-18
insufficient statistics data R-18
integer rank
matrix 15-12
deleting list items 16-3
displaying 16-4
integer scaling 2-14, 2-15
integral
displaying list elements 16-4
editing 16-3
definite 13-6
indefinite 13-23
finding statistical values in list ele-
ments 16-9
integration 13-6
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generate a series 16-8
list function syntax 16-6
list variables 16-1
returning position of element in
16-8
trigonometry 13-19
enclosing arguments 1-21
negative numbers in 1-20
reversing order in 16-9
sending and receiving 16-6
sorting elements 16-9
storing elements 16-1, 16-4, 16-5
storing one element 16-6
logarithm 13-4
addition and subtraction 15-6
logarithmic
fit 10-13
arithmetic operations in 15-6
assembly from vectors 15-1
changing row position 18-25
column norm 15-10
functions 13-3
logical operators
AND 13-19
equals (logical test) 13-19
greater than 13-19
greater than or equal to 13-19
IFTE 13-19
condition number 15-11
create identity 15-13
creating 15-3
less than 13-18
less than or equal to 13-18
NOT 13-19
creating in Home 15-5
not equal to 13-19
OR 13-19
deleting columns 18-24
XOR 13-19
logistic fit 10-13
display eigenvalues 15-11
displaying 15-5
loop commands
displaying matrix elements 15-5
dot product 15-11
BREAK 18-24
DO...UNTIL...END 18-23
FOR I= 18-24
WHILE...REPEAT...END 18-23
extracting a portion 18-25
loop functions
ITERATE 13-10
RECURSE 13-10
summation 13-11
low battery 1-1
matrix calculations 15-1
lowercase letters 1-6
multiplying by vector 15-7
multiplying row by value and add-
ing result to second row 18-25
multiplying row number by value
18-25
negating elements 15-8
opening Matrix Editor 18-28
raised to a power 15-7
redimension 18-25
replacing portion of matrix or vec-
tor 18-25
sending or receiving 15-4
M
mantissa 13-15
math functions
complex number 13-7
hyperbolic 13-10
in menu map R-13
keyboard 13-3
logical operators 13-18
menu 1-7
polynomial 13-11
probability 13-12
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singular value decomposition
15-13
angle measure 1-10
number format 1-10
plotting to find 7-7
singular values 15-13
size 15-12
spectral norm 15-13
spectral radius 15-13
start Matrix Editor 18-24
storing elements 15-3, 15-5
storing matrix elements 15-6
swap column 18-25
swap row 18-25
transposing 15-13, 15-14
variables 15-1
natural log plus 1 13-10
matrix functions 15-10
COLNORM 15-10
COND 15-11
CROSS 15-11
DET 15-11
negative numbers 1-20
no equations checked R-19
Normal Z-distribution, confidence in-
DOT 15-11
EIGENVAL 15-11
EIGENVV 15-11
IDENMAT 15-11
INVERSE 15-11
LQ 15-11
LSQ 15-11
LU 15-12
MAKEMAT 15-12
QR 15-12
RANK 15-12
ROWNORM 15-12
RREF 15-12
creating notes 17-6
SCHUR 15-12
SIZE 15-12
SPECNORM 15-13
SPECRAD 15-13
SVD 15-13
SVL 15-13
TRACE 15-13
TRN 15-13
fixed 1-10
maximum real number 1-22, 13-8
fraction 1-11
in Solve aplet 7-5
mixed fraction 1-11
scientific 1-10
memory R-18
clearing all R-3
organizing 14-9
out of R-19
Standard 1-10
numeric precision 14-9
Numeric view
saving 1-25, 19-1
viewing 14-1
menu lists
adding values 2-18
automatic 2-16
build your own table 2-19
display defining function for col-
umn 2-17
searching 1-8
minimum real number 13-8
mixed fraction format 1-11
modes
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recalculating 2-18
integer scaling 2-14
one-variable statistics 10-18
overlaying 2-15, 4-3
scaling 2-13
setup 2-16, 2-19
O
off
automatic 1-1
power 1-1
on/cancel 1-1
One-Proportion Z-Interval 11-17
One-Sample T-Interval 11-18
One-Sample T-Test 11-12
One-Sample Z-Interval 11-15
One-Sample Z-Test 11-8
order of precedence 1-21
overlaying plots 2-15, 4-3
split-screen view 2-14
splitting into plot and close-up
splitting into plot and table 2-13
statistical data 10-15
statistics parameters 10-18
P
tickmarks 2-6
π 13-8
tracing 2-8
paired columns 10-11
parametric variables
axes 18-32
two-variable statistics 10-18
plotting resolution
plot-view variables
area 18-32
connect 18-32
grid 18-33
in menu map R-8
indep 18-33
labels 18-34
recenter 18-34
ycross 18-37
parentheses
to close arguments 1-21
to specify order of operation 1-21
pause 18-30
isect 18-34
permutations 13-12
pictures
attaching in Sketch view 17-3
plot
s1mark-s5mark 18-35
analyzing statistical data in 10-19
auto scale 2-14
tracing 18-33
umin/umax 18-36
ustep 18-36
box-and-whisker 10-16
cobweb 6-1
polar variables
comparing 2-5
connected points 10-17, 10-19
decimal scaling 2-14
defining the independent variable
18-36
axes 18-32
connect 18-32
grid 18-33
in menu map R-9
indep 18-33
drawing axes 2-7
expressions 3-3
labels 18-34
grid points 2-7
recenter 18-34
histogram 10-15
ycross 18-37
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polynomial
halt program execution 18-30
insert line breaks 18-29
prevent screen display being up-
set date and time 18-28
store keycode 18-29
coefficients 13-11
evaluation 13-11
form 13-11
roots 13-12
Taylor 13-7
polynomial functions
POLYCOEF 13-11
POLYEVAL 13-11
POLYFORM 13-11
POLYROOT 13-12
ports 19-5
position argument 18-21
power (x raised to y) 13-5
precedence 1-22
predicted values
statistical 10-20
print
Q
function 3-4
in program names 18-4
contents of display 18-26
name and contents of variable
18-26
minimum 13-8
real-number functions 13-13
object in history 18-26
variables 18-26
probability functions
! 13-12
COMB 13-12
RANDOM 13-13
UTPC 13-13
UTPF 13-13
UTPN 13-13
UTPT 13-13
program
commands 18-4
MIN 13-15
copying 18-8
creating 18-4
debugging 18-7
deleting 18-9
delimiters 18-1
TRUNCATE 13-16
XPON 13-17
editing 18-5
naming 18-4
recalculation for table 2-18
receive error R-19
receiving
pausing 18-30
printing 18-26
sending and receiving 18-8
structured 18-1
prompt commands
beep 18-26
aplet 19-5
lists 16-6
matrices 15-4
programs 18-8
create choose box 18-26
create input form 18-29
display item 18-27
display message box 18-29
redrawing
table of numbers 2-17
reduced row echelon 15-12
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regression
sequence variables
analysis 10-17
fit models 10-13
formula 10-12
Grid 18-33
user-defined fit 10-13
relative error
Recenter 18-34
statistical 10-18
resetting
serial port connectivity 19-5
aplet 19-3
calculator R-3
memory R-3
result
time 18-28
sign reversal 7-6
sine 13-4
copying to edit line 1-22
reusing 1-22
root
inverse hyperbolic 13-9
interactive 3-10
nth 13-6
variable 18-34
root-finding
displaying 7-7
interactive 3-9
operations 3-10
variables 3-10
creating a blank graphic 18-23
creating a set of 17-5
S
sets 17-5
S1mark-S5mark variables 18-35
scaling
slope 3-10
automatic 2-14
decimal 2-10, 2-14
integer 2-10, 2-14, 2-15
options 2-13
resetting 2-13
error messages 7-7
initial guesses 7-5
trigonometric 2-14
scatter plot 10-15, 10-17
connected 10-17, 10-19
SCHUR decomposition 15-12
scientific number format 1-10, 1-20
scrolling
plotting to find guesses 7-7
setting number format 7-5
solve variables
in Trace mode 2-8
axes 18-32
searching
connect 18-32
menu lists 1-8
fastres 18-32
speed searches 1-8
grid 18-33
secant 13-20
in menu map R-11
indep 18-33
sending
aplets 19-4
labels 18-34
lists 16-6
recenter 18-34
programs 18-8
ycross 18-37
sequence
sorting 19-6
definition 2-2
aplets in alphabetic order 19-6
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aplets in chronological order 19-6
elements in a list 16-9
spectral norm 15-13
spectral radius 15-13
square root 13-5
stack history
storing
printing 18-26
stairsteps graph 6-1
standard number format 1-10
statistics
16-6
value 14-2
analysis 10-1
analyzing plots 10-19
angle mode 10-12
literal in symbolic operations
calculate one-variable 18-30
calculate two-variable 18-30
data set variables 18-41
data structure 18-41
define one-variable sample 18-30
define two-variable data set’s de-
pendent column 18-31
define two-variable data set’s in-
dependent column 18-31
defining a fit 10-12
defining a regression model
10-12
summation function 13-11
calculations in Function aplet
defining expressions 2-1
differentiation 13-21
displaying definitions 3-8
evaluating variables in view 2-3
symbolic functions
deleting data 10-11
editing data 10-10
frequency 18-30
inserting data 10-11
plot type 10-18
ISOLATE 13-17
plotting data 10-15
predicted values 10-20
regression curve (fit) models
10-12
QUAD 13-18
saving data 10-10
sorting data 10-11
specifying angle setting 10-12
toggling between one-variable
and two-variable 10-12
tracing plots 10-19
troubleshooting with plots 10-19
zooming in plots 10-19
statistics variables
table
navigate around 3-8
numeric values 3-7
numeric view setup 2-16
tangent 13-4
Axes 18-32
inverse hyperbolic 13-9
Taylor polynomial 13-7
θrng 2-6
θstep 2-6
tickmarks for plotting 2-6
time 13-14
Connect 18-32
Grid 18-33
Hmin/Hmax 18-33
Hwidth 18-33
in menu map R-12
Indep 18-33
I-11
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setting 18-28
time, converting 13-14
times sign 1-20
upper-tail Snedecor’s F 13-13
tmax 18-36
tmin 18-36
too few arguments R-19
tracing
regression fit 10-13
functions 2-8
more than one curve 2-8
not matching plot 2-8
plots 2-8
recall 14-3
transmitting
lists 16-6
matrices 15-4
programs 18-8
transposing a matrix 15-13
Triangle Solver aplet 9-1
trigonometric
in Symbolic view 2-3
fit 10-13
functions 13-19
scaling 2-10, 2-14, 2-15
trigonometry functions
ACOT 13-19
step size of independent 18-37
use in calculations 14-3
VARS menu 14-4, 14-5
vectors
ACSC 13-20
ASEC 13-20
COT 13-20
CSC 13-20
SEC 13-20
trng 2-6
truncating values to decimal places
13-16
column 15-1
tstep 2-6, 18-37
Two-Proportion Z-Interval 11-17
Two-Proportion Z-Test 11-11
Two-Sample T-Interval 11-19
Two-Sample T-test 11-14
Two-Sample Z-Interval 11-16
typing letters 1-6
configuration 1-18
W
warning symbol 1-8
where command ( | ) 13-18
U
X
undefined
Xcross variable 18-37
xrng 2-6
name R-19
result R-19
un-zoom 2-11
Y
upper-tail chi-squared probability
13-13
Ycross variable 18-37
yrng 2-6
upper-tail normal probability 13-13
I-12
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options within a table 2-17
out 2-9
Z
Z-Interval 11-15
zoom 2-17
axes 2-12
redrawing table of numbers op-
tions 2-17
square 2-10
un-zoom 2-11
box 2-9
center 2-9
within Numeric view 2-17
X-zoom 2-9
examples of 2-11
factors 2-13
in 2-9
Y-zoom 2-10
options 2-9, 3-8
I-13
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