HP (Hewlett Packard) 39G User Manual

HP 39G/40G  
GRAPHING CALCULATOR  
USER’S GUIDE  
Version 1.1  
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..........................................................................................1-9  
Setting a mode ................................................................................1-11  
Aplets (E–lessons)................................................................................1-11  
Aplet library....................................................................................1-15  
Aplet views .....................................................................................1-15  
Aplet view configuration ................................................................1-17  
Mathematical calculations....................................................................1-18  
Using fractions......................................................................................1-24  
Complex numbers.................................................................................1-27  
Catalogs and editors .............................................................................1-28  
Differences between the HP 38G and the HP 39G/40G.......................1-29  
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 ..............................2-14  
About the numeric view..................................................................2-16  
Setting up the table (numeric view setup) ......................................2-17  
Exploring the table of numbers.......................................................2-18  
Building your own table of numbers ..............................................2-19  
“Build Your Own” menu keys........................................................2-20  
Example: plotting a circle...............................................................2-21  
Contents  
i
3 Function aplet  
About the Function aplet ........................................................................3-1  
Getting started with the Function aplet.............................................3-1  
Function aplet interactive analysis .........................................................3-8  
Plotting a piecewise defined function example ..............................3-11  
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...........................................................................7-8  
Using variables in equations.................................................................7-10  
8 Statistics aplet  
About the Statistics aplet........................................................................8-1  
Getting started with the Statistics aplet.............................................8-1  
Entering and editing statistical data........................................................8-5  
Defining a regression model (2VAR).............................................8-11  
Computed statistics...............................................................................8-13  
Plotting .................................................................................................8-15  
Plot types.........................................................................................8-16  
Fitting a curve to 2VAR data..........................................................8-17  
Setting up the plot (Plot setup view)...............................................8-18  
Trouble-shooting a plot...................................................................8-19  
Exploring the graph ........................................................................8-20  
Calculating predicted values...........................................................8-21  
ii  
Contents  
9 Inference aplet  
About the Inference aplet .......................................................................9-1  
Getting started with the Inference aplet............................................9-2  
Importing Sample Statistics from the Statistics aplet.......................9-5  
Hypothesis tests......................................................................................9-9  
One–Sample Z–Test .........................................................................9-9  
Two–Sample Z–Test.......................................................................9-10  
One–Proportion Z–Test ..................................................................9-11  
Two–Proportion Z–Test..................................................................9-12  
One–Sample T–Test .......................................................................9-13  
Two–Sample T–Test.......................................................................9-14  
Confidence intervals.............................................................................9-16  
One–Sample Z–Interval..................................................................9-16  
Two–Sample Z–Interval .................................................................9-17  
One–Proportion Z–Interval.............................................................9-18  
Two–Proportion Z–Interval ............................................................9-19  
One–Sample T–Interval..................................................................9-20  
Two–Sample T–Interval .................................................................9-21  
10 Using mathematical functions  
Math functions......................................................................................10-1  
The MATH menu............................................................................10-1  
Math functions by category..................................................................10-3  
Keyboard functions.........................................................................10-4  
Calculus functions...........................................................................10-7  
Complex number functions.............................................................10-8  
Constants.........................................................................................10-9  
Hyperbolic trigonometry.................................................................10-9  
List functions ................................................................................10-10  
Loop functions..............................................................................10-11  
Matrix functions............................................................................10-11  
Polynomial functions ....................................................................10-12  
Probability functions.....................................................................10-13  
Real-number functions..................................................................10-15  
Statistics-Two ...............................................................................10-18  
Symbolic functions .......................................................................10-19  
Test functions................................................................................10-20  
Trigonometry functions ................................................................10-21  
Symbolic calculations.........................................................................10-22  
Finding derivatives .......................................................................10-23  
Contents  
iii  
11 Variables and memory management  
Introduction ..........................................................................................11-1  
Storing and recalling variables .............................................................11-2  
The VARS menu ..................................................................................11-4  
Memory Manager.................................................................................11-9  
12 Matrices  
Introduction ..........................................................................................12-1  
Creating and storing matrices...............................................................12-2  
Working with matrices .........................................................................12-4  
Matrix arithmetic..................................................................................12-6  
Solving systems of linear equations................................................12-8  
Matrix functions and commands ..........................................................12-9  
Argument conventions..................................................................12-10  
Matrix functions............................................................................12-10  
Examples ............................................................................................12-13  
13 Lists  
Creating lists.........................................................................................13-1  
Displaying and editing lists ..................................................................13-4  
Deleting lists ...................................................................................13-6  
Transmitting lists ............................................................................13-6  
List functions........................................................................................13-7  
Finding statistical values for list elements..........................................13-10  
14 Notes and sketches  
Introduction ..........................................................................................14-1  
Aplet note view.....................................................................................14-1  
Aplet sketch view .................................................................................14-3  
The notepad ..........................................................................................14-6  
iv  
Contents  
15 Programming  
Introduction ..........................................................................................15-1  
Program catalog ..............................................................................15-2  
Creating and editing programs .............................................................15-4  
Using programs ....................................................................................15-7  
Working with programs........................................................................15-8  
About customizing an aplet..................................................................15-9  
Aplet naming convention..............................................................15-10  
Customizing an aplet example......................................................15-10  
Programming commands....................................................................15-14  
Aplet commands ...........................................................................15-14  
Branch commands.........................................................................15-17  
Drawing commands ......................................................................15-19  
Graphic commands .......................................................................15-20  
Loop commands............................................................................15-22  
Matrix commands .........................................................................15-23  
Print commands ............................................................................15-25  
Prompt commands ........................................................................15-25  
Stat-One and Stat-Two commands ...............................................15-29  
Storing and retrieving variables in programs................................15-30  
Plot-view variables .......................................................................15-30  
Symbolic-view variables...............................................................15-37  
Numeric-view variables................................................................15-39  
Note variables ...............................................................................15-42  
Sketch variables ............................................................................15-42  
16 Extending aplets  
Creating new aplets based on existing aplets .......................................16-1  
Resetting an aplet............................................................................16-4  
Annotating an aplet with notes .......................................................16-4  
Annotating an aplet with sketches ..................................................16-4  
Downloading e-lessons from the web ..................................................16-4  
Sending and receiving aplets................................................................16-5  
Sorting items in the aplet library menu list ..........................................16-6  
Contents  
v
Reference information  
Regulatory information .........................................................................R-1  
USA .................................................................................................R-1  
Canada .............................................................................................R-1  
LED safety.............................................................................................R-2  
Warranty................................................................................................R-2  
CAS .......................................................................................................R-4  
Resetting the HP 39G/40G ....................................................................R-4  
To erase all memory and reset defaults ...........................................R-5  
If the calculator does not turn on ....................................................R-5  
Glossary.................................................................................................R-6  
Operating details....................................................................................R-7  
Batteries ...........................................................................................R-7  
Menu maps of the VARS menu.............................................................R-8  
Home variables......................................................................................R-8  
Function aplet variables.........................................................................R-9  
Parametric aplet variables....................................................................R-10  
Polar aplet variables ............................................................................R-11  
Sequence aplet variables......................................................................R-12  
Solve aplet variables............................................................................R-13  
Statistics aplet variables ......................................................................R-14  
Menu maps of the MATH menu .........................................................R-15  
Math functions ...............................................................................R-15  
Program constants..........................................................................R-17  
Program commands .......................................................................R-18  
Selected status messages .....................................................................R-19  
Index  
vi  
Contents  
Preface  
The HP 39G/40G is a feature-rich graphing calculator. It is  
also a powerful mathematics learning tool. The HP 39G/40G  
is designed so that you can use it to explore mathematical  
functions and their properties.  
You can get more information on the HP 39G/40G 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:  
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 key first, are represented as follows:  
CLEAR,  
MODES,  
ACOS, etc.  
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  
Preface  
P-1  
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 merchantaiblity 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.  
Hewlett-Packard Company 2000, all rights reserved.  
The programs that control your HP 39G/40G are copyrighted  
and all rights are reserved. Reproduction, adaptation or  
translation of those programs without prior written permission  
of Hewlett Packard is prohibited.  
P-2  
Preface  
1
Getting started  
On/off, cancel operations  
To turn on  
To cancel  
Press  
to turn on the calculator.  
When the calculator is on, the  
operation.  
key cancels the current  
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.  
Getting started  
1-1  
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.  
this picture. “Press  
is the label for the first menu key in  
” 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 (ꢀ  
symbolsindicate whether there is more history in the HOME  
display. Press the *e,ꢀand *k,ꢀto scroll in the HOME display.  
N O T E  
The HP 40G is packaged with a computerized algebra system  
(CAS). Press  
This User’s Guide contains images from the HP39G and do  
not display the menu key label.  
to access the computerized algebra system.  
1-2  
Getting started  
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  
Menu key  
labels  
Menu keys  
Aplet control  
keys  
Cursor  
keys  
Alpha key  
Shift key  
Enter key  
Getting started  
1-3  
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 1-15.  
Displays the Plot view for the current  
aplet. See “Plot view” on page 1-15.  
Displays the Numeric view for the  
current aplet. See “Numeric view” on  
page 1-15.  
Displays the HOME view. See  
“HOME” on page 1-1.  
Displays the Aplet Library menu. See  
“Aplet library” on page 1-15.  
Displays the VIEWS menu. See “Aplet  
views” on page 1-15.  
1-4  
Getting started  
Entry/Edit keys  
The entry and edit keys are:  
Key  
Meaning  
Cancels the current operation if the  
calculator is on by pressing  
(CANCEL)  
.
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  
as a menu key,  
as pressing  
or  
is present  
acts the same  
.
or  
Enters a negative number. To enter  
–25, press 25. Note: this is not the  
same operation that the subtract  
button performs ( ).  
5
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.  
CLEAR  
Clears all data on the screen. On a  
settings screen, for example Plot  
Setup,  
CLEAR returns allsettings  
to their default values.  
*>,, *A,, *k,,  
Moves the cursor around the display.  
Press  
first to move to the  
*e,  
beginning, end, top or bottom.  
CHARS  
Displays a menu of all available  
characters. To type one, use the arrow  
keys to highlight it, and press  
select multiple characters, select each  
and press , then press  
. To  
.
Getting started  
1-5  
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 labelled in blue above the  
key). You do not need to hold  
down  
This action is depicted in this manual as  
“press  
when you press HOME.  
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.  
HELPWITH  
Example  
The HP 39G 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  
commands such as sine, cosine, and tangent before  
invoking the HELPWITH command.  
1-6  
Getting started  
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  
to  
trigonometric (like  
) functions. Press  
complete the operation:  
256  
displays 16.  
.
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 (*e,, *k,) and  
move from the category list in the left column to the  
item list in the right column (*>,, *A,).  
Press  
line.  
to insert the selected command onto the edit  
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.  
Pressing  
MATH menu.  
takes you to the beginning of the  
See “Math functions by category” on page 10-3 for details of  
the math functions.  
H I N T  
When using the MATH menu, or any menu on the HP 39G/  
40G, 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 15-14.  
Inactive keys  
If you press a key that does not operate in the current context,  
!
a warning symbol like this  
appears. There is no beep.  
Getting started  
1-7  
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 *e, or *k, to scroll through the list. If you press  
*e, or  
or the beginning of the list. Highlight the item you want  
to select, then press (or ).  
*k,, you’ll go all the way to the end  
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 (with no edit line), 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  
*>,. To go down a  
page, press  
*A,.  
To cancel a menu  
Press  
operation.  
(for CANCEL) or  
. This cancels the current  
1-8  
Getting started  
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 (  
). Some input forms include items  
to check ( ). See below for an example of an input form.  
Reset input  
form values  
To reset a default field value in an input form, move the cursor  
to that field and press  
the input form, press  
. To reset all default field values in  
CLEAR.  
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  
Setting  
MODES to access the HOME MODES input form.  
Options  
Angle  
Angle values are:  
Measure  
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.  
Getting started  
1-9  
Setting  
Options (Continued)  
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.  
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 1-24.  
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.  
1-10  
Getting started  
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  
The cursor (highlight) is in  
the first field, Angle  
Measure.  
2. Press  
to display a  
list of choices.  
3. Press*k,ꢀ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:  
Built-in the HP 39G/40G (initial purchase).  
Aplets created by saving existing aplets, which have been  
modified, with specific configurations. See “Creating  
new aplets based on existing aplets” on page 16-1.  
Downloaded from HP’s Calculators web site.  
Copied from another calculator.  
Getting started  
1-11  
Aplets are stored in the Aplet  
library. See “Aplet library” on  
page 1-15 for further  
information.  
You can modify configuration  
settings for the graphical, tabular, and symbolic views of the  
aplets in the following table. See “Aplet view configuration”  
on page 1-17 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  
Polar  
Parametric relations x and y in terms of t.  
Example: x = cos(t) and y = sin(t).  
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  
U
n 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 .  
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 39G/40G 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 charge and  
transferred to the HP 39G/40G using the separately supplied  
Connectivity Kit.  
1-12  
Getting started  
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.  
When first started, the aplet is  
in  
mode, in which the  
arrow keys, the  
keys and the  
and  
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 (see right).  
Pressing the *A,ꢀand *>,ꢀkey moves between sub-  
expressions, while pressing the *k,ꢀandꢀ*e, key changes  
their values.  
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  
answer and provide feedback. An  
for those who give up!  
button evaluates the  
button is provided  
Getting started  
1-13  
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.  
When the user presses  
in the  
view, the screen  
shown right is displayed.  
In this mode, the graph  
controls the equation. Pressing  
the *k,*e, and *>,*A, keys  
transforms the graph, with  
these transformations reflected  
in the equation.  
The button labelled  
toggle between  
. When  
is a  
and  
is  
Origin  
chosen, the ‘point of control’ is  
at the origin (0,0) and the  
*k,*e, and *>,*A, keys  
control vertical and horizontal  
transformations. 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  
amplitude and frequency of the  
graph. This is most easily seen  
by experimenting.  
Extremum  
Pressing  
displays the  
equation at the top of the  
screen. The equation is  
controls the graph. Pressing the  
*A, and *>, keys moves from  
parameter to parameter.  
Pressing the *k, or *e, key changes the parameter’s values.  
The default angle setting for this aplet is radians. The angle  
setting can be changed to degrees by pressing  
.
1-14  
Getting started  
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).  
Symbolic 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.  
Plot view  
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.  
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 2-15 for further  
information.  
Getting started  
1-15  
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)  
without erasing any pre-  
existing plot(s).  
See “Other views for scaling and splitting the graph” on  
page 2-13 for further information.  
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 14-1 for further  
information.  
Sketch view  
Press  
SKETCH to display the aplet’s sketch view.  
1-16  
Getting started  
Displays pictures to  
supplement an aplet.  
See “Notes and sketches” on  
page 14-1 for further  
information.  
Aplet view configuration  
You use the SETUP keys (  
configure the aplet. For example, press  
)to display the input form for setting the aplet’s  
, and  
) to  
SETUP-PLOT  
(
plot settings. Angle measure is controlled using the MODES  
view.  
Plot Setup  
Press  
SETUP-PLOT. Sets  
parameters to plot a graph.  
Numeric Setup Press  
SETUP-NUM. Sets  
parameters for building a table  
of numeric values.  
Symbolic  
Setup  
This view is only available in  
the Statistics aplet in 2VAR  
mode, where it plays an  
important role in choosing data  
models. Press (  
SETUP  
SYMB.  
To change views  
Each view is a separate environment. To change a view, 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, and  
transfer the aplet to other HP 39G/40G calculators. See  
“Sending and receiving aplets” on page 16-5.  
Getting started  
1-17  
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 15-14 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 39G/40G 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.  
232 14 8  
---------------------------  
Example  
Calculate  
ln(45) :  
–3  
23 ꢁ,  
14  
8  
j
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 *k, to highlight  
it and then press  
.
Negative  
numbers  
Type  
sign.  
to start a negative number or to insert a negative  
To raise a negative number to a power, enclose it in  
2
2
parentheses. For example, (–5) = 25, whereas –5 = –25.  
1-18  
Getting started  
Scientific  
notation  
(powers of 10)  
A number like 5 × 104 or 3.21 × 107 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 using  
10 N .)  
(4 × 1013)(6 × 1023  
)
----------------------------------------------------  
Example  
Calculate  
3 × 10–5  
4
EEX  
13  
6
j 3  
EEX  
EEX  
23  
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.  
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.  
Getting started  
1-19  
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 39G/40G calculates  
according to the order of algebraic precedence (the next  
topic). Following are some examples using parentheses.  
Entering...  
Calculates...  
sin (45 + π)  
sin (45) + π  
85 × 9  
45  
45  
π
π
85  
9
85  
9
85 × 9  
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 39G/40G can represent is  
–499  
1 × 10  
(1E–499). A smaller result is displayed as zero. The  
–49  
largest number is 9.99999999999 × 10 . A larger result is  
still displayed as this number.  
1-20  
Getting started  
Clearing  
numbers  
clears the character under the cursor. When the  
cursor is positioned after the last character,  
the character to the left of the cursor, that is, it performs  
the same as a backspace key.  
deletes  
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  
When you highlight a previous input or result (by pressing  
*k,), the  
and  
menu labels appear.  
To copy a  
previous line  
Highlight the line (press *k,) and press  
expression) is copied into the edit line.  
. The number (or  
To reuse the last  
result  
Press  
HOME display into an expression. ANS is a variable that is  
updated each time you press  
ANS (last answer) to put the last result from the  
.
To repeat a  
previous line  
To repeat the very last line, just press  
. Otherwise,  
highlight the line (press *k,) first, and then press  
highlighted expression or number is re-entered. If the  
previous line is an expression containing the ANS, the  
calculation is repeated iteratively.  
. The  
Getting started  
1-21  
Example  
See how  
and  
ANS retrieves and reuses the last result (50),  
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  
,
,
j , (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-  
21 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.  
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  
evaluates (or re-evaluates) the last input,  
whereas pressing  
the edit line.  
ANS copies the last result (as ANS) into  
1-22  
Getting started  
Storingavalue  
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 11,  
“Variables and memory management” for more information  
on variables. For example:  
1. Perform a calculation.  
45  
8
8 3  
2. Store the result in the A variable.  
A
3. Perform another calculation using the A variable.  
95  
2
A
Accessing the  
display history  
Pressing *k, 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  
*k,, *e,  
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  
Getting started  
1-23  
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 Fractions, as follows:  
Setting  
1. In HOME, open the HOME MODES input form.  
Fraction mode  
MODES  
2. Select Number Format and press  
options, then select Fraction.  
to display the  
*e,  
*e,*e,*e,*e,  
3. Press  
to select the  
option, then select the precision value.  
*A,  
4. Enter the precision that you want to use, and press  
to  
set the precision. Press  
to return to HOME.  
See “Setting fraction precision” below for more  
information.  
1-24  
Getting started  
Setting  
fraction  
precision  
The fraction precision setting determines the precision in  
which the HP 39G/40G 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:  
Precision set to 1:  
Precision set to 2:  
Precision set to 3:  
Precision set to 4  
Getting started  
1-25  
Fraction  
When entering fractions:  
calculations  
You use the j key to separate the numerator part and  
the denominator part of the fraction.  
1
To enter a mixed fraction, for example, 1 / , you enter it  
2
1
in the format (1+ / ).  
2
For example, to perform the following calculation:  
3
7
3(2 / + 5 / )  
4
8
1. Set the mode Number format to fraction.  
MODES *e,  
Select  
Fraction  
*A,4  
2. Return to HOME and enter the calculation.  
3
2
3
j 4  
j 8  
5
7
3. Evaluate the calculation.  
Converting  
decimals to  
fractions  
To convert a decimal value to a fraction:  
1. Set the number mode to 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.  
1-26  
Getting started  
Converting a  
number to a  
fraction  
When converting a number 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.  
In this example, the  
fraction precision is set  
to 6.  
Complex numbers  
Complex results  
The HP 39G/40G 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  
I
press  
, *k,or *e,keys to select Constant, *A,ꢀ  
to move to the right column of the menu, *e,ꢀtoselect i,  
and  
.
Getting started  
1-27  
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  
Catalogs and editors  
The HP 39G/40G 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 14, “Notes and sketches”.  
(
SKETCH)  
List (  
LIST)  
Lists. In HOME, lists are enclosed  
in {}. See Chapter 13, “Lists”.  
Matrix  
(
One- and two-dimensional arrays.  
In HOME, arrays are enclosed in  
[]. See Chapter 12, “Matrices”.  
MATRIX)  
Notepad  
Notes (short text entries). See  
Chapter 14, “Notes and sketches”.  
(
NOTEPAD)  
Program  
Programs that you create, or  
associated with user-defined  
aplets. See Chapter 15,  
“Programming”.  
(
PROGRAM)  
1-28  
Getting started  
Differences between the HP 38G and the  
HP 39G/40G  
CAS  
The HP 40G is packaged with a computer algebra system  
(CAS). Refer to the CAS Manual for further information.  
Memory  
manager  
The HP 39G/40G incorporates a memory manager that you  
can use to see how much memory the objects that you have  
created or loaded are occupying. See “Memory Manager” on  
page 11-9 for more information.  
Plot Goto  
function  
In Plot view, you can use the  
menu key to jump to a  
value on the plot instead of having to trace the plot to locate  
values. See “Exploring the graph” on page 2-7 for more  
information.  
Statistics Pred  
function  
When you choose the  
view screen, it is now possible to  
option in the Statistics aplet’s Plot  
along the regression  
curve. Once a data set and regression curve is displayed,  
pressing the up and down arrows will move between the data  
and the curve of regression. When the regression curve is  
selected, the values displayed in the Plot view status line are  
the PREDYvalues. On the HP 38G, the Trace function would  
select known data points only.  
Inference aplet To complement the Statistics aplet, a new Inference aplet has  
been added. Use this aplet to perform hypothesis tests and  
determine confidence intervals. See “About the Inference  
aplet” on page 9-1 for more information.  
Trig Explorer  
and Quadratic  
Explorer  
The teaching aplets Trig Explorer and Quadratic Explorer  
have been added to the calculator. These two aplets add  
powerfully to the capabilities of the calculator in the  
classroom.  
aplets  
Getting started  
1-29  
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 *k,or*e, 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.  
. All selected  
Aplets and their views  
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 and  
second terms for U  
(U1, or...U9, or U0).  
Define the nth term  
of the sequence in  
terms of N or of the  
prior terms, U(N–1) and 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.  
2-2  
Aplets and their views  
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).  
*k,  
4. Press  
Note how the values for  
F1(X) and F2(X) are  
substituted into F3(X).  
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.  
Aplets and their views  
2-3  
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  
done.  
when  
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  
5 key on the keyboard.  
Enters the independent variable in the  
Parametric aplet. Or, you can use the  
5 key on the keyboard.  
Enters the independent variable in the  
Polar aplet. Or, you can use the  
key on the keyboard.  
5
Enters the independent variable in the  
Sequence aplet. Or, you can use the  
5 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 arithmetric expressions.  
Displays a menu for entering variable  
names or contents of variables.  
Displays the menu for entering math  
operations.  
Displays special characters. To enter  
one, place the cursor on it and press  
. To remain in the CHARS menu  
and enter another special character,  
CHARS  
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.  
2-4  
Aplets and their views  
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  
your choice, and press or  
, highlight  
. As a shortcut  
to  
, just highlight the field to change and press  
to cycle through the options.  
If there is an option to select or deselect, press  
to check or uncheck it.  
2. Press  
to view more settings.  
3. When done, press  
to view the new plot.  
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  
Parametric aplet: Specifies the t-  
values (T) for the graph.  
θRNG  
Polar aplet: Specifies the angle (θ)  
value range for the graph.  
Aplets and their views  
2-5  
Field  
Meaning (Continued)  
NRNG  
Sequence aplet: Specifies the index  
(N) values for the graph.  
TSTEP  
For Parametric plots: the increment  
for the independent variable.  
θSTEP  
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  
to display the second page.  
Field  
Meaning  
SIMULT  
If more than one relation is being  
plotted, plots them simultaneously  
(otherwise sequentially).  
INV. CROSS  
CONNECT  
Cursor crosshairs invert the status of  
the pixels they cover.  
Connect the plotted points. (The  
Sequence aplet always connects  
them.)  
LABELS  
Label the axes with XRNGand YRNG  
values.  
AXES  
GRID  
Draw the axes.  
Draw grid points using XTICKand  
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  
.
2-6  
Aplets and their views  
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.  
*>,  
*A,  
Moves cursor to far left or far right.  
*k,  
*e,  
Moves cursor between relations.  
or  
Interrupts plotting.  
Continues plotting if interrupted.  
Turns menu-key labels on and off. When  
the labels are off, pressing  
them back on.  
turns  
Pressing  
full row of labels.  
Pressing a second time  
once displays the  
removes the row of labels to display  
only the graph.  
Pressing  
a third time displays  
the coordinate mode.  
Displays ZOOM menu list.  
Turns trace mode on/off. A white box  
appears over the on  
.
Opens an input form for you to enter anX  
(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 3-3.  
Displays the current, defining  
expression. Press  
menu.  
to restore the  
Aplets and their views  
2-7  
Trace a graph  
You can trace along a function using the *>, or*A, 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 *k, or *e,  
to move between relations.  
To jump directly  
to a value  
To jump straight to a value rather than using the Trace  
function, use the  
value. Press  
menu key. Press  
to jump to the value.  
, then enter a  
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  
plot on a larger or smaller scale. It is a shortcut for changing  
the Plot Setup.  
. Zooming redraws the  
With the Set Factors option you can specify the factors that  
determine the extent of zooming, and whether the zoom is  
centered about the cursor.  
ZOOM options  
Press  
displayed, press  
all aplets.  
, select an option, and press  
. (If  
is not  
.) Not all  
options are available in  
Option  
Meaning  
Center  
Re-centers the plot around the current  
position of the cursor without  
changing the scale.  
Box...  
Lets you draw a box to zoom in on. See  
“Other views for scaling and splitting  
the graph” on page 2-13.  
2-8  
Aplets and their views  
Option  
Meaning (Continued)  
In  
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  
X-Zoom Out  
Y-Zoom In  
Y-Zoom Out  
Square  
Divides horizontal scale only, using  
X–factor.  
Multiplies horizontal scale, using  
X–factor.  
Divides vertical scale only, using  
Y–factor.  
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. 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.)  
Aplets and their views  
2-9  
Option  
Meaning (Continued)  
Integer  
Rescales horizontal axis only, making  
each pixel =1 unit. (Not available in  
Sequence or Statistics aplets.)  
Trig  
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.)  
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  
(Press *k, to move to the  
bottom of the Zoom list.)  
Zoom Out:  
Out  
Now un-zoom.  
2-10  
Aplets and their views  
X-Zoom In:  
X-Zoom In  
Now un-zoom.  
X-Zoom Out:  
X-Zoom Out  
Now un-zoom.  
Y-Zoom In:  
Y-Zoom In  
Now un-zoom.  
Y-Zoom Out:  
Y-Zoom Out  
Zoom Square:  
Square  
Aplets and their views  
2-11  
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  
to turn on the menu-key labels.  
2. Press and select .  
3. Position the cursor on one corner of the rectangle. Press  
.
4. Use the cursor keys  
(*e,, etc.) to drag to the  
opposite corner.  
5. Press  
to zoom in on  
the boxed area.  
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.  
2-12  
Aplets and their views  
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).  
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.)  
Aplets and their views  
2-13  
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  
or  
, select the zoom method and press  
. 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).  
*>, moves the leftmost cursor to the screen’s  
left edge and  
*A, 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  
*A, cursor keys. These  
keys move the trace point left or right along the plot, and  
in the table, the corresponding values are highlighted.  
3. To move between functions, use the *k, and *e, cursor  
keys to move the cursor from one graph to another.  
4. To return to a full Numeric (or Plot) view, press  
(or  
).  
2-14  
Aplets and their views  
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.  
About the numeric view  
After entering and selecting  
(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.  
Aplets and their views  
2-15  
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  
menu key allows you to make  
the table match the pixel columns in the graph view.  
2. When done, press to view the table of numbers.  
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.  
2-16  
Aplets and their views  
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.  
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 NUMZOOM  
factor in Numeric Setup.  
Decimal  
Changes intervals for the independent  
variable to 0.1 units. Starts at zero.  
(Shortcut to changing NUMSTARTand  
NUMSTEP.)  
Integer  
Trig  
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 degrees  
1
or 8 / grads. Starts at zero.  
3
Un-zoom  
Returns the display to the previous  
zoom.  
Aplets and their views  
2-17  
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.  
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  
enter them in order, because the  
. You do not have to  
function can  
rearrange them. To insert a number between two others,  
use  
.
F1 and F2  
entries are  
generated  
automatically  
You enter  
numbers into  
the X column  
2-18  
Aplets and their views  
Clear data  
Press  
CLEAR,  
to erase the data from a table.  
“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 row of zero values 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.  
CLEAR  
Clears all data from the table.  
Aplets and their views  
2-19  
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  
1. In the Function aplet, specify the functions.  
Select  
Function  
5
9
9
5
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.  
2-20  
Aplets and their views  
3
Function aplet  
About the Function aplet  
The Function aplet enables you to explore up to 10  
real–valued, rectangular functions y in terms of x. For  
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  
1. Open the Function aplet.  
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.  
Function aplet  
3-1  
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 to clear all lines.)  
1
5
5
3
2
Set up the plot  
You can change the scales of the x and y axes, graph  
resolution, and spacing of 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  
CLEAR to restore the default values.  
4. Specify a grid for the graph.  
*A,ꢀ*e,ꢀ*e,ꢀ  
Plot the  
5. Plot the functions.  
functions  
3-2  
Function aplet  
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.  
*k,  
Analyse graph  
with FCN  
9. Display the Plot view menu.  
functions  
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 3-9 for further information.  
Function aplet  
3-3  
To find the  
greater of the two  
roots of the  
quadratic  
10. Find the greater of the two roots of the quadratic  
function.  
Note: Move the cursor to the graph of the quadratic  
equation by pressing the *k,ꢀor *e,ꢀkey. Then move the  
cursor so that it is near x = –1 by pressing the *A,ꢀorꢀ  
*>,ꢀkey.  
function  
Select Root  
The root value is  
displayed at the bottom  
of the screen.  
To find the  
11. Find the intersection of the two functions.  
intersection of  
the two functions  
*e,ꢀ  
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.  
3-4  
Function aplet  
To find the slope  
of the quadratic  
function  
13. Find the slope of the quadratic function at the intersection  
point.  
SelectSlopeꢀ  
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  
15. Move the cursor to x = –1 by pressing the *A,ꢀor *>,ꢀ  
key.  
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.  
2
The cursor jumps to  
x = –2 on the linear  
function.  
Function aplet  
3-5  
18. Display the numerical value of the integral.  
Note: See “Shading  
area” on page 3-10 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.  
*k,ꢀ  
Select Extremum  
The coordinates of the  
extremum are displayed  
at the bottom of the  
screen.  
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  
20. Display the numeric view.  
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.  
3-6  
Function aplet  
22. Match the table settings to the pixel columns in the graph  
view.  
Explore the  
table  
23. Display a table of numeric values.  
To navigate  
24. Move to X = –5.9.  
around a table  
*e,ꢀ6 timesꢀ  
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: NUMZOOMhas  
a setting of 4.  
In  
Function aplet  
3-7  
To change font  
size  
27. Display table numbers in large font.  
To display the  
symbolic  
28. Display the symbolic definition for the F1 column.  
*A,ꢀ  
definition of a  
column  
The symbolic definition of  
F1 is displayed at the bottom  
of the screen.  
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 3-9. 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.  
3-8  
Function aplet  
Access FCN  
variables  
The FCN variables are contained in the VARS menu.  
To access FCN variables in HOME:  
Select Plot FCN  
*A,ꢀ  
*k,or*e, to choose a  
variable  
To access FCN variable in the Function aplet’s Symbolic  
view:  
Select Plot FCN  
*A,ꢀ  
*k,or*e, to choose a variable  
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.  
Function aplet  
3-9  
Function  
Description (Continued)  
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.  
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  
to plot the functions.  
4. Press *>, or *A, to position the cursor at the starting  
point of the area you want to shade.  
5. Press  
6. Press  
7. Press  
.
, then select Signed areaand press  
, choose the function that will act as the  
.
boundary of he shaded area, and press  
8. Press the *>, or *A,ꢀkey to shade in the area.  
9. Press 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.  
.
3-10  
Function aplet  
Plotting a piecewise defined function example  
Suppose you wanted to graph 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
j
CHARS ≤  
1
j
CHARS >  
1
AND  
CHARS 1  
4
j
CHARS > 1  
Note: You can use the  
menu key to assist in the  
entry of equations. It has  
the same effect as  
pressing  
5 .  
Function aplet  
3-11  
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  
2. Enter each equation.  
expressions  
3
5
3
5
Parametric aplet  
4-1  
Set angle  
measure  
3. Set the angle measure to degrees.  
MODES  
Select Degrees  
Set up the plot  
4. Display the graphing options.  
PLOT  
You can see 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.  
*A,ꢀ360  
5ꢀ  
Plot the  
6. Plot the expression.  
expression  
7. To see all the circle, press  
twice.  
4-2  
Parametric aplet  
Overlay plot  
8. Plot a triangle graph over the existing circle graph.  
PLOT  
*e,  
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 numeric values.  
You can see there is a  
column of t-values.  
This column is active in  
the sense that 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 2-18 for further information.  
Parametric aplet  
4-3  
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
j
5
2
5
Specify plot  
settings  
3. Specify the plot settings. In this example, we will use the  
default settings, except for the θRNGfields.  
SETUP-PLOT  
CLEAR  
*A,ꢀ4ꢀ  
π
Plot the  
4. Plot the expression.  
expression  
Polar aplet  
5-1  
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 θ for 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 2-18 for further information.  
5-2  
Polar aplet  
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.  
Getting started with the Sequence aplet  
The following example defines and then plots an expression  
in the Sequence aplet.  
Open the  
Sequence  
aplet  
1. Open the Sequence aplet.  
Select  
Sequence  
The Sequence aplet  
starts in the Symbolic  
view.  
Sequence aplet  
6-1  
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 menu  
,
keys to assist in the entry  
of equations.  
Specify plot  
settings  
3. In Plot Setup, first set the SEQPLOToption to  
Stairstep. Reset the default plot settings by clearing  
the Plot Setup view.  
A Stairsteps graph plots n on the horizontal axis and  
n
U on the vertical axis.  
A Cobweb graph plots U on the horizontal axis  
n-1  
and U on the vertical axis.  
n
SETUP-PLOT  
CLEAR  
*e,ꢀ*A,ꢀ8ꢀ  
*A,ꢀ8ꢀ  
6-2  
Sequence aplet  
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 numeric values for this example.  
Sequence aplet  
6-3  
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, that is, 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 matrices or graphs in the Function aplet.  
Solve aplet  
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  
1. Open the Solve aplet.  
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 menu key to assist in the entry of  
equations.  
Define known  
variables  
3. Display the Solve numeric view screen.  
4. Enter the values for the known variables.  
2 7  
1 6  
7 8  
6 7  
*e,  
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  
(
.
7-2  
Solve aplet  
Solve the  
unknown  
variable  
5. Solve for the unknown variable (A).  
*e,ꢀ*e,ꢀ  
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 2.47  
2
m/s .  
Because the variable A in the equation is linear, once  
values are substituted into V, U and D, we know that we  
need not look for any other solutions.  
Plot the  
equation  
The Plot view shows one graph for each member of the  
selected equation. You can choose any of the variables in  
the Numeric view to be the independent variable.  
The other variables take on the values assigned to them in  
the Numeric view. The current equation is  
V2 = U2 + 2AD . With the variable A highlighted, the  
Plot view will show two graphs.  
One of these is Y = V2 , with V = 27.78 , or  
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 , or Y = 200A + 277.8889 . This graph is  
also a line. The desired solution is the value of A where  
these two lines intersect.  
6. Plot the equation for variable A.  
Select Auto  
Scale  
Solve aplet  
7-3  
7. Trace along the graph representing the left member of the  
equation until the cursor nears the intersection.  
*A,ꢀ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 before using the Numeric  
view Solve option. See “Plotting to find guesses” on  
page 7-8 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  
when done.  
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.  
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.  
7-4  
Solve aplet  
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  
. Solve starts looking for a solution at  
the initial guess.  
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 guesses” on  
page 7-8 for further information.  
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 1-9 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  
7-5  
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  
to clear the message.  
Message  
Condition  
Zero  
The Solve aplet found a point where  
the value of the equation (or the root of  
the expression) is zero within the  
calculator’s 12-digit accuracy.  
Sign Reversal  
Solve found two points where the  
value of the equation has opposite  
signs, but it cannot find a point in  
between where the value is 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  
is closer to zero. If the value of the  
equation is a continuous real function,  
this point is Solve’s best  
approximation of an actual root.  
Extremum  
Solve found a point where the value of  
the equation approximates a local  
minimum (for positive values) or  
maximum (for negative values). This  
point may or may not be a root. Or:  
Solve stopped searching at  
9.99999999999E499, the largest  
number the calculator can represent.  
7-6  
Solve aplet  
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  
guess.  
) and start over with a different initial  
Solve aplet  
7-7  
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:  
at2  
2
-------  
x = v0t +  
where x is distance, v is initial velocity, t is time, and a is  
0
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
j 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
*e,4  
*e,*e, to highlight T  
7-8  
Solve aplet  
3. Use the Plot view to find an initial guess for T. First set  
appropriate X and Y ranges in the Plot Setup. Since we  
have an equation,X = V × T + A × T2 2 , the plot will  
produce two graphs: one for Y = X and one for  
Y = V × T + A × T2 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  
*e,  
5
35  
4. Plot the graph.  
5. Move the cursor near the positive (right-side)  
intersection. This cursor value will be an initial guess for  
T.  
*A,ꢀto move cursor to  
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.  
Solve aplet  
7-9  
8. 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 an  
initial guess.  
3
*k,*k,*k,  
50  
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 everywhere whenever it is  
recalculated.  
H I N T  
As the Solve aplet uses any 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, you define  
2
F1(X)=X +10, you can enter F1(X)=50in the Solve aplet  
2
to solve the equation X +10=50.  
7-10  
Solve aplet  
8
Statistics aplet  
About the Statistics aplet  
The Statistics aplet can store up to ten separate data sets at one  
time. It can do 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  
Statistics aplet  
8-1  
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
*A, to move to the next  
column  
1400  
1100  
2890  
920  
2265  
2200  
8-2  
Statistics aplet  
Choose fit and  
data columns  
4. Select a fit in the Symbolic setup view.  
SETUP-SYMB  
*e,ꢀ  
Select Linear  
You can define 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 C1 and C2.  
Explore  
statistics  
6. Find the mean advertising time (MEANX) and the mean  
sales (MEANY).  
MEANXis about 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.  
*e,ꢀ9 times  
The value is 0.8995 to  
four significant digits.  
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  
*A, 7  
100  
4000  
Statistics aplet  
8-3  
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.  
*e,ꢀto move to the FIT1  
field  
The full FIT1  
expression is shown. The  
slope (m) is 425.875.  
The y-intercept (b) is about 376.25.  
8-4  
Statistics aplet  
Predict values  
13. To find the predicted sales figure if advertising were to  
go up to 6 minutes:  
S (to highlight  
Stat-Two)  
*A,*e, (to highlight  
PREDY)  
6
14. Return to the Plot view.  
15. Jump to the indicated point on the regression line.  
*e,ꢀ  
6
Observe the predicted y-  
value in the left bottom  
corner of the screen.  
Entering and editing statistical data  
The Numeric view (  
) is used to enter data into the  
Statistics aplet. Each column represents a variable named C0  
to 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  
8-5  
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.  
Deletes the currently highlighted  
value.  
CLEAR  
Clears the current column or all  
columns of data. Press  
CLEAR to  
display a menu list, then select the  
current column or all columns option,  
and press  
.
FXUVRUꢀ Moves to the first or last row, or first or  
NH\  
last column.  
8-6  
Statistics aplet  
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 reads  
. Press  
to  
see the statistics  
calculated from the sample data in C1. Press the *e,ꢀkeyꢀ  
to scroll to further statistics.  
Note that the title for 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, H1 is automatically set to use C1 for 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.  
Statistics aplet  
8-7  
4. Press  
statistics window and  
press key to see  
to close the  
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.  
ꢀRUꢀ  
Typing aid for the column variables  
( ) or for the Fit expressions ( ).  
Displays the current variable  
expression in standard mathematical  
form. Press  
when done.  
Evaluates the variables in the  
highlighted column (C1, etc.)  
expression.  
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.  
8-8  
Statistics aplet  
Key  
Meaning (Continued)  
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)  
160  
Frequency  
5
3
8
2
1
165  
170  
175  
180  
5. Move the highlight bar  
into the right column of  
the H1 definition and  
replace the frequency  
value of 1 with the name  
C2.  
2
6. Return to the numeric view.  
7. Enter the frequency data shown in the above table.  
*A,ꢀ5  
3
8
2
1
Statistics aplet  
8-9  
8. Display the computed  
statistics.  
You can scroll down to  
the mean. 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.  
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.  
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  
aplet or HOME.  
), or you can switch to another  
Edit a data set  
Delete data  
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 line for modification. Press  
after modifying the value on the edit line.  
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  
CLEAR. Select the column name.  
To delete all columns of data, press  
CLEAR. Select  
All columns.  
8-10  
Statistics aplet  
Insert data  
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. Select the SORTORDERoption. You can choose either  
Ascendingor Descending.  
3. Specify the INDEPENDENTand DEPENDENTdata  
columns. Sorting is by the independent column. For  
instance, if Age is C1 and Income is C2 and you want to  
sort by Income, then you make C2 the independent  
column for the sorting and C1 the dependent column.  
To sort just one column, choose Nonefor the  
dependent column.  
For one-variable statistics with two data columns,  
specify the frequency column as the dependent  
column.  
4. Press  
.
Defining a regression model (2VAR)  
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.  
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 (S1FIT to S5FIT) you  
want to define.  
3. Press  
and select from the following list. Press  
when done. The regression formula for the fit is  
displayed in Symbolic view.  
Statistics aplet  
8-11  
Fit models  
Eight 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  
Fits to a logarithmic curve,  
y = m lnx + b.  
mx  
Exponential  
Power  
Fits to an exponential curve, y = be  
.
m
Fits to a power curve, y = bx .  
Quadratic  
Fits to a quadratic curve,  
y = ax +bx+c. Needs at least three  
2
points.  
Cubic  
Fits to a cubic curve,  
y = ax +bx +cx+d. Needs at least  
3
2
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.  
UserDefined 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.  
8-12  
Statistics aplet  
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  
MINΣ  
Q1  
Sample standard deviation of data set.  
Minimum data value in data set.  
First quartile: median of ordinals to  
left of median.  
MEDIAN  
Q3  
Median value of data set.  
Third quartile: median of ordinals 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 Q1and Q3in  
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.  
Statistics aplet  
8-13  
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.  
8-14  
Statistics aplet  
Plotting  
You can plot:  
histograms (  
)
box-and-whisker plots (  
scatter plots of data (  
)
).  
Once you have entered your data (  
), defined your data  
set (  
), and defined your Fit model for two-variable  
statistics (  
SETUP-SYMB), you can plot your data. You  
can select up to five scatter or box-and-whisker plots at a time.  
You can plot only one histogram at a time.  
To plot statistical  
data  
1. In Symbolic view (  
you want to plot.  
), select (  
) the data sets  
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 with the HWIDTHsetting.  
4. Press  
. If you have not adjusted the Plot Setup  
select Auto Scale  
yourself, you can try  
.
H I N T  
Auto Scale can be relied upon to give a good starting scale  
which can then be adjusted in the Plot Setup view.  
Statistics aplet  
8-15  
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 *A,ꢀkey.  
Box and  
Whisker Plot  
One-variable statistics. The  
left whisker marks the  
minimum data value. The box  
marks the first quartile, the  
median, and the third quartile.  
The right whisker marks the  
maximum data value.  
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 *A, to move to the next  
data point and display  
information about it.  
To connect the data points as  
they are plotted, checkmark  
CONNECT in the second page  
of the Plot Setup. This is not a  
regression curve.  
8-16  
Statistics aplet  
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 8-11.  
The expression in Fit2  
shows that the  
slope=1.98082191781and  
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, CORRrelates to the linear model.  
Relative Error  
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.  
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.  
H I N T  
In order to access these variables after you plot a set of  
statistics, you must press  
to access the numeric view  
and then to display the correlation values. The values  
are stored in the variables when you access the Symbolic  
view.  
Statistics aplet  
8-17  
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 “Setting up the plot (Plot view setup)” on page 2-5.  
Settings unique to the Statistics aplet are as follows:  
Plot type (1VAR)  
Histogram width  
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).  
Histogram range  
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  
highlighted setting.  
to change the  
Connected points 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. 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).  
(2VAR)  
8-18  
Statistics aplet  
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.  
Statistics aplet  
8-19  
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.  
*>,  
*A,  
Moves cursor to far left or far right.  
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/off. Turning  
draws a curve to fit the data points  
according to the current regression  
model.  
on  
(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  
labels.  
redisplays the menu  
8-20  
Statistics aplet  
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 *e, to move to the regression curve.  
3. Press  
and enter the value of X. The cursor jumps to  
the desired point on curve and the coordinate display  
shows X and the predicted value of Y.  
In HOME,  
Enter PREDX(y-value)  
to find the predicted (estimated) value for the  
independent variable given a hypothetical dependent  
value.  
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  
PREDYfunction 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.  
Statistics aplet  
8-21  
9
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.  
Inference aplet  
9-1  
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  
1. Open the Inference aplet.  
Inference aplet  
Select Inferential  
.
The Inference aplet opens  
in the Symbolic view.  
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 P, the Z–Test  
on 1 proportion  
Z–Int: 1 P, the confidence  
interval for 1 proportion, based  
on the Normal distribution  
Z: P – P , the  
Z–Int: P – P , the confidence  
1
2
1
2
Z–Test on the  
difference in two  
proportions  
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–Int: µ µ , the confidence  
1
2
1
2
T–Test on the  
difference of two  
means  
interval for the difference of two  
means, based on the Student’s  
t–distribution  
9-2  
Inference aplet  
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.  
Define the  
inferential  
method  
1. Select the Hypothesis Testinferential method.  
Select HYPOTH TEST  
2. Define the type of test.  
*e,  
Z–Test: 1 µ  
3. Select an alternative hypothesis.  
*e,  
µ< µ 0  
Inference aplet  
9-3  
Enter data  
4. Enter the sample statistics and population parameters that  
define the chosen test or interval.  
SETUP-NUM  
The table below lists the fields in this view for our current  
Z–Test: 1 µ example.  
Field name  
Definition  
µ0  
Assumed population mean  
Population standard deviation  
Sample mean  
σ
x
n
Sample size  
α
Alpha level for the test  
By default, each field already contains a value. These  
values constitute the example database and are explained  
in the  
feature of this aplet.  
Displayon-line  
help  
5. Display the on-line help.  
6. To close the on-line help,  
press  
.
Display test  
results in  
numeric  
format  
7. 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.  
9-4  
Inference aplet  
Plot test  
results  
8. 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 statistic. The rejection  
R
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.  
A calculator produces the following 6 random numbers:  
0.529, 0.295, 0.952, 0.259, 0.925, and 0.592  
Open the  
1. Open Statistics aplet. Note: Reset current settings.  
Statistics aplet  
Select  
Statistics  
The Statistics aplet opens  
in the Numeric view.  
Inference aplet  
9-5  
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  
its menu label.  
is displayed as  
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.  
Open  
6. Open the Inference aplet and clear current settings.  
Inference aplet  
Select  
Inference  
9-6  
Inference aplet  
Choose  
inference  
method and  
type  
7. Choose an inference method.  
SelectCONF INTERVAL  
8. Choose a distribution statistic type.  
*e,ꢀ  
Select T-Int: 1 µ  
Set up the  
interval  
calculation  
9. Set up the interval calculation. Note: The default values  
are sample data from the on-line help example.  
SETUP-NUM  
Import the data 10. Import the data from the Statistics aplet. Note: The data  
from C1 is displayed by default.  
Note: If there are other  
columns of data in the  
Statistics aplet, you could  
select a column and 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.  
Inference aplet  
9-7  
11. Specify a 90% confidence interval in the C:field.  
*e,*e,*e, to move to the  
C:field  
0.9  
Display  
Numeric view  
12. Display the confidence interval in the Numeric view.  
Note: The interval setting is 0.5.  
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.  
9-8  
Inference aplet  
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 39G/40G 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 1 mean  
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:  
H1µ < µ0  
H1:µ > µ0  
H1:µ ≠ µ0  
Inputs  
The inputs are:  
Field name  
Definition  
x
Sample mean.  
n
Sample size.  
µ
Hypothetical population mean.  
Population standard deviation.  
Significance level.  
0
σ
α
Inference aplet  
9-9  
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 : µ = µ ).  
0
1
2
You select one of the following alternative hypotheses against  
which to test the null hypothesis:  
H1µ1 < µ2  
H1µ1 > µ2  
H1µ1 ≠ µ2  
Inputs  
The inputs are:  
Field name  
Definition  
Sample 1 mean.  
x1  
Sample 2 mean.  
x2  
n1  
n2  
σ1  
σ2  
α
Sample 1 size.  
Sample 2 size.  
Population 1 standard deviation.  
Population 2 standard deviation.  
Significance level.  
9-10  
Inference aplet  
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: 1P  
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. H0π = π0  
You select one of the following alternative hypotheses against  
which to test the null hypothesis:  
H1:π < π0  
H1:π > π0  
H1:π ≠ π0  
Inputs  
The inputs are:  
Field name  
Definition  
x
Number of successes in the sample.  
Sample size.  
n
π
α
Population proportion of successes.  
Significance level.  
Inference aplet  
9-11  
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: P1–P2  
On the basis of statistics from two samples, each from a  
different population, the 2 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.  
(H : π = π ).  
0
1
2
You select one of the following alternative hypotheses against  
which to test the null hypothesis:  
H1π1 < π2  
H1π1 > π2  
H1π1 ≠ π2  
Inputs  
The inputs are:  
Field name  
Definition  
;1  
X2  
n1  
n2  
α
Sample 1 mean.  
Sample 2 mean.  
Sample 1 size.  
Sample 2 size.  
Significance level.  
9-12  
Inference aplet  
Results  
The results are:  
Result  
Description  
Test P1–P2  
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  
Inputs  
The inputs are:  
Field name  
Definition  
Sample mean.  
x
Sx  
n
Sample standard deviation.  
Sample size.  
µ0  
α
Hypothetical population mean.  
Significance level.  
Inference aplet  
9-13  
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  
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  
9-14  
Inference aplet  
Inputs  
The inputs are:  
Field name Definition  
Sample 1 mean.  
x1  
Sample 2 mean.  
x2  
S1  
Sample 1 standard deviation.  
Sample 2 standard deviation.  
Sample 1 size.  
S2  
n1  
n2  
Sample 2 size.  
α
Significance level.  
_Pooled?  
Check this option to pool samples based on  
their standard deviations.  
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.  
Inference aplet  
9-15  
Confidence intervals  
The confidence interval calculations that the HP 39G/40G can  
perform are based on the Normal Z–distribution or Student’s  
t–distribution.  
One–Sample Z–Interval  
Menu name  
Z–INT: 1 µ  
This option uses the Normal Z–distribution to calculate a  
confidence interval for µ, the true mean of a population, when  
the true population standard deviation, σ, is known.  
Inputs  
The inputs are:  
Field name Definition  
Sample mean.  
x
σ
n
Population standard deviation.  
Sample size.  
C
Confidence level.  
Results  
The results are:  
Result  
Critical Z  
µ min  
Description  
Critical value for Z.  
Lower bound for µ.  
Upper bound for µ.  
µ max  
9-16  
Inference aplet  
Two–Sample Z–Interval  
Menu name  
Z–INT: µ1µ2  
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 name Definition  
Sample 1 mean.  
x1  
Sample 2 mean.  
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 .  
∆µ Min  
1
2
Upper bound for µ µ .  
∆µ Max  
1
2
Inference aplet  
9-17  
One–Proportion Z–Interval  
Menu name  
Z–INT: 1 P  
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 name Definition  
x
Sample success count.  
Sample size.  
n
C
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  
9-18  
Inference aplet  
Two–Proportion Z–Interval  
Menu name  
Z–INT: P1 – P2  
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 name Definition  
Sample 1 success count.  
Sample 2 success count.  
x1  
x2  
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.  
∆π Min  
Upper bound for the difference between the  
proportions of successes.  
∆π Max  
Inference aplet  
9-19  
One–Sample T–Interval  
Menu name  
T–INT: 1 µ  
This option uses the Student’s t–distribution to calculate a  
confidence interval for µ, the true mean of a population, for  
the case in which the true population standard deviation, σ, is  
unknown.  
Inputs  
The inputs are:  
Field name Definition  
Sample mean.  
x
Sx  
n
Sample standard deviation.  
Sample size.  
C
Confidence level.  
Results  
The results are:  
Result  
Critical T  
µ Min  
Description  
Critical value for T.  
Lower bound for µ.  
Upper bound for µ.  
µ Max  
9-20  
Inference aplet  
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, µ − µ , when the population standard  
1
2
deviations, σ and σ , are unknown.  
1
2
Inputs  
The inputs are:  
Field name Definition  
Sample 1 mean.  
x 1  
Sample 2 mean.  
x 2  
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.  
Results  
The results are:  
Result  
Description  
Critical T  
Critical value for T.  
Lower bound for µ µ .  
∆µ Min  
1
2
Upper bound for µ µ .  
∆µ Max  
1
2
Inference aplet  
9-21  
10  
Using mathematical functions  
Math functions  
The HP 39G/40G 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 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  
functions. The menu key  
, you see the menu list of Math  
indicates that the MATH  
FUNCTIONS menu list is active.  
Using mathematical functions  
10-1  
To select a  
function  
1. Press  
to display the MATH menu. The categories  
appear in alphabetical order. Press *e, or *k, 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.  
2. The list of functions (on the right) applies to the currently  
highlighted category (on the left). Use *A, 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  
Stat–Two  
(Two–variable  
statistics)  
Complex  
numbers  
Matrices  
Polynomial  
Probability  
Real–numbers  
Symbolic  
Tests  
Constant  
Hyperbolic trig  
Lists  
Trigonometry  
10-2  
Using mathematical functions  
Math functions by category  
Following are definitions for all categories of functions except  
List, Matrix, and Statistics, each of which appears in its own  
chapter. Except for the keyboard operations, which do not  
appear in the MATH menu, all other functions are listed by  
their category in the MATH menu.  
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 menus.  
π
For a description, see “p” on  
page 10-9.  
ARG  
For a description, see “ARG” on  
page 10-8.  
For a description, see “D” on  
page 10-7.  
AND  
!
For a description, see “AND” on  
page 10-21.  
For a description, see “!” on  
page 10-13.  
For a description, see “S” on  
page 10-11.  
EEX  
For a description, see “Scientific  
notation (powers of 10)” on  
page 1-19.  
)
For a description, see “S” on  
page 10-7.  
The multiplicative inverse function  
finds the inverse of a square matrix,  
and the multiplicative inverse of a  
real or complex number. Also  
works on a list containing only  
these object types.  
x1  
Using mathematical functions  
10-3  
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  
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).  
10-4  
Using mathematical functions  
–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).  
–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)  
Using mathematical functions  
10-5  
* N,  
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  
n
Takes the nth root of x.  
root NTHROOT value  
Example  
3NTHROOT8 returns 2  
10-6  
Using mathematical functions  
Calculus functions  
The symbols for differentiation and integration are available  
directly form the keyboard— and ) respectively—as  
well as from the MATH menu.  
%
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 10-23.  
%variable(expression)  
Example  
2
%s1(s1 +3*s1)returns 2*s1+3  
)
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 10-22 for further  
details.  
Example  
)(0,s1,2*X+3,X)  
*k,  
finds the  
indefinite result 3*s1+2*(s1^2/2)  
See “To find the indefinite integral using formal  
variables” on page 10-25 for more information on  
finding indefinite integrals.  
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.  
Using mathematical functions  
10-7  
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  
Imaginary part, y, of a complex number, (x,y).  
IM ((x,y))  
Example  
IM((3,4)) returns 4  
RE  
Real part x, of a complex number, (x,y).  
RE((x,y))  
Example  
RE((3,4)) returns 3  
10-8  
Using mathematical functions  
Constants  
The HP 39G/40G has an internal numeric representation for  
these constants.  
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 1 × 10499  
.
MINREAL  
π
Internally represented as 3.14159265359.  
π
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  
Hyperbolic tangent.  
TANH(value)  
Using mathematical functions  
10-9  
ALOG  
EXP  
Antilogarithm (exponential). This is more accurate than  
10^xdue to limitations of the power function.  
ALOG(value)  
Natural exponential. This is more accurate than ex due to  
limitations of the power function.  
EXP(value)  
x
EXPM1  
LNP1  
Exponent minus 1 : e –1. This is more accurate than EXP  
when x is close to zero.  
EXPM1(value)  
Natural log plus 1 : ln(x+1). This is more accurate than the  
natural logarithm function when x is close to zero.  
LNP1(value)  
List functions  
These functions work on list data. See “List functions” on  
page 13-7.  
10-10  
Using mathematical functions  
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-n,term1,term2)  
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).  
Σ
Summation. Finds the sum of expression with respect to  
variable from initialvalue to finalvalue.  
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 12-9.  
Using mathematical functions  
10-11  
Polynomial functions  
Polynomials are products of constants (coefficients) and  
variables raised to powers (terms).  
POLYCOEF  
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.  
POLYEVAL  
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.  
POLYFORM  
POLYROOT  
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.  
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].  
10-12  
Using mathematical functions  
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!(nr)).  
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!/ (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.  
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  
Using mathematical functions  
10-13  
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 a χ  
random variable is greater than value.  
2
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)  
10-14  
Using mathematical functions  
Real-number functions  
Some real-number functions can also take complex  
arguments.  
CEILING  
Smallest integer greater than or equal to value.  
CEILING(value)  
Examples  
CEILING(3.2) returns 4  
CEILING(-3.2) returns -3  
DEGRAD  
Degrees to radians. Converts value from Degrees angle  
format to Radians angle format.  
DEGRAD(value)  
Example  
DEGRAD(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  
Using mathematical functions  
10-15  
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.x format (number of hours or degrees 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  
MIN  
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  
Minimum. The lesser of two values.  
MIN(value1,value2)  
Example  
MIN(210,25)returns 25  
10-16  
Using mathematical functions  
MOD  
Modulo. The remainder of value1/value2.  
value1 MODvalue2  
Example  
9 MOD 4 returns 1  
%
x percent of y; that is, x/100*y.  
%(x,y)  
Example  
%(20,50) returns 10  
%CHANGE  
%TOTAL  
RADDEG  
ROUND  
Percent change from x to y, that is, 100(y–x)/x.  
%CHANGE(x,y)  
Example  
%CHANGE(20,50) returns 150  
Percent total : (100)y/x. What percentage of x is y.  
%TOTAL(x,y)  
Example  
%TOTAL(20,50) returns 250  
Radians to degrees. Converts value from radians to degrees.  
RADDEG(value)  
Example  
RADDEG(π) returns 180  
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 7.68  
ROUND (0.0036757,-3) returns 0.00368  
Using mathematical functions  
10-17  
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  
XPON  
Exponent of value.  
XPON(value)  
Example  
XPON(123.4) returns 2  
Statistics-Two  
These are functions for use with two-variable statistics. See  
“Two-variable” on page 8-14.  
10-18  
Using mathematical functions  
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 10-  
20.)  
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?  
QUAD  
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  
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  
Using mathematical functions  
10-19  
QUOTE  
Encloses an expression that should not be evaluated  
numerically.  
QUOTE(expression)  
Examples  
QUOTE(SIN(45))  
F1(X) stores the expression  
SIN(45) rather than the value of SIN(45).  
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.  
value1value2  
= =  
Equals (logical test). Returns 1 if true, 0 if false.  
value1==value2  
>
Not equal to. Returns 1 if true, 0 if false.  
value1value2  
Greater than. Returns 1 if true, 0 if false.  
value1>value2  
Greater than or equal to. Returns 1 if true, 0 if false.  
value1value2  
10-20  
Using mathematical functions  
AND  
IFTE  
Compares value1 and value2. Returns 1 if they are both non-  
zero, otherwise returns 0.  
value1 AND value2  
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  
ACSC  
ASEC  
COT  
Arc cotangent.  
ACOT(value)  
Arc cosecant.  
ACSC(value)  
Arc secant.  
ASEC(value)  
Cotangent: cosx/sinx.  
COT(value)  
CSC  
Cosecant: 1/sinx  
CSC(value)  
SEC  
Secant: 1/cosx.  
SEC(value)  
Using mathematical functions  
10-21  
Symbolic calculations  
The HP 39G/40G 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 39G/40G 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 39G/40G 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:  
(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 10-24 for an example.  
calculations in  
the Function  
aplet  
10-22  
Using mathematical functions  
Finding derivatives  
The HP 39G/40G can perform symbolic differentiation on  
some functions. There are two ways of using the HP 39G/40G  
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
S1  
2. Evaluate the function.  
3. Show the result.  
*k,ꢀ  
HP 39G  
HP 40G  
Using mathematical functions  
10-23  
To find  
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 :  
derivatives in the  
Function aplet’s  
Symbolic view  
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.  
*k,  
4. Press  
to display the result. (Use the arrow keys to  
view the entire function.)  
HP 39G  
HP 40G  
You could also just define  
F1(x)= dx( sin(x2) + 2cos(x)) .  
10-24  
Using mathematical functions  
To find the  
For example, to find the indefinite integral of  
3x2 5dx use:  
indefinite integral  
using formal  
variables  
(0, S1, 3X2 5, X)  
1. Enter the function.  
0
S1  
X
3
5
X
H I N T  
If the Decimal Mark setting in the Modes input form  
(
MODES)is set to Comma, use  
instead of  
.
2. Show the result format.  
*k,  
3. Press  
to close the  
show window.  
4. Copy the result and evaluate.  
HP 39G  
HP 40G  
Thus, substituting X for S1, it can be seen that:  
x3  
----  
3
3x2 5dx= – 5x + 3  
---------------  
X  
(X)  
This result derives 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
Using mathematical functions  
10-25  
The ‘extra’ constant of 6.4  
results from the substitution  
5
of x = 0 into (x – 2) /5,  
and should be disregarded if  
an indefinite integral is  
required.  
10-26  
Using mathematical functions  
11  
Variables and memory management  
Introduction  
The HP 39G/40G has approximately 232K of user memory.  
The calculator uses this memory to store variables, perform  
computation, and store history.  
A variable is an object that you create in memory to hold data.  
The HP 39G/40G 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.  
Variables and memory management  
11-1  
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  
.
11-2  
Variables and memory management  
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
8
6
8 3  
2. Move the highlight to the result you wish to store.  
3. Press  
4. Press  
to copy the result to the command line.  
.
5. Enter a name for the variable.  
*k,ꢀ  
A
6. Press  
to store the result.  
The results of a calculation can also be stored directly to a  
variable. For example:  
2
8
5 j 3  
B
To recall a value  
To recall a variable’s value, type the name of the variable and  
press  
.
A
Variables and memory management  
11-3  
To use variables  
in calculations  
You can use variables in calculations. The calculator  
substitutes the variable’s value in the calculation:  
65  
A
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.  
*A,  
4. Use the arrow keys to select the variable that you want.  
For example, to select the M2 variable, press *e,.  
*e,  
11-4  
Variables and memory management  
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  
*e,ꢀto select L2  
Variables and memory management  
11-5  
4. Enter data for L2.  
55  
90  
48  
77  
86  
5. Press  
to access HOME.  
6. Open the variable menu and select L1.  
*e,*e,*e,*A,  
7. Copy it to the command line. Note: Because the  
option is highlighted, the variables name, rather than its  
contents, is copied to the command line.  
8. Insert the + operator and select the L2 variable from the  
List variables.  
*e,*e,*e,*A,*e,  
9. Store the answer in the List catalog L3 variable.  
L3  
Note: You can also type  
list names directly from the keyboard.  
11-6  
Variables and memory management  
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.  
Category Available names  
Complex  
Z0 to Z9  
For example, (1,2)  
Z0 or 2+3i  
Z1. You can enter a complex number by  
typing (r,i), where r represents the real part,  
and i represents the imaginary part.  
Graphic  
G0 to G9  
See “Graphic commands” on page 15-20 for  
more information on storing graphic objects  
via programming commands. See “To store  
into a graphics variable” on page 14-5 for  
more information on storing graphic object  
via the sketch view.  
Library  
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.  
Modes variables store the modes settings that  
L1.  
Matrix  
Modes  
you can configure using  
MODES.  
Notepad  
Program  
Real  
Notepad variables store notes.  
Program variables store programs.  
A to Z and θ.  
For example, 7.45  
A.  
Variables and memory management  
11-7  
Aplet variables 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-9.  
Parametric  
Polar  
X0, Y0 to X9, Y9 (Symbolic view). See  
“Parametric aplet variables” on page R-10.  
R0 to R9 (Symbolic view). See “Polar  
aplet variables” on page R-11.  
Sequence  
Solve  
U0 to U9 (Symbolic view). See “Sequence  
aplet variables” on page R-12.  
E0 to E9 (Symbolic view). See “Solve  
aplet variables” on page R-13.  
Statistics  
C0 to C9 (Numeric view). See “Statistics  
aplet variables” on page R-14.  
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 *A, to access the variables in the right  
column.  
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.)  
6. To copy the value of the  
variable into the edit line,  
press  
.
and press  
11-8  
Variables and memory management  
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.  
*e,ꢀ*e,ꢀ*e,  
3. To delete variables in a category:  
Press  
to delete the selected variable.  
Press  
selected category.  
CLEAR to delete all variables in the  
Variables and memory management  
11-9  
12  
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 in MODES is set to Comma, then the  
row separators are periods.)  
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.  
Matrices  
12-1  
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])&M1  
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 opens  
an empty matrix with the highlighted  
name.  
Transmits the highlighted matrix to  
another HP 39G/40G or a disk drive.  
See “Sending and receiving aplets” on  
page 16-5.  
Receives a matrix from another  
HP 39G/40G or a disk drive. See  
“Sending and receiving aplets” on  
page 16-5.  
Clears the highlighted matrix.  
Clears all matrices.  
CLEAR  
*e, or  
Moves to the end or the beginning of  
the catalog.  
*k  
12-2  
Matrices  
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 Real  
vectoror 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 Real  
matrix 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.  
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.  
Matrices  
12-3  
To transmit a  
matrix  
You can send matrices between calculators just as you can  
send aplets, programs, lists, and notes.  
1. Align the HP 39G calculators’ infrared ports.  
2. Open the Matrix catalogs on both calculators.  
3. Highlight the matrix to send.  
4. Press  
5. Press  
.
on the receiving calculator.  
Matrices can also be transmitted to or from a computer a cable  
and Connectivity Kit.  
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  
at all.  
does not advance  
Switches between larger and smaller  
font sizes.  
Deletes the highlighted cells, row, or  
column (you are prompted to make a  
choice).  
CLEAR  
Clears all elements from the matrix.  
*k, *e, Moves to the first row, last row, first  
*A,*>,  
column, or last column respectively.  
12-4  
Matrices  
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  
M2 is [[3,4],[5,6]], then M2(1,2) returns 4.  
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.  
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.  
Matrices  
12-5  
Matrix arithmetic  
You can use the arithmetic functions (+, –, ×, / ) 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 four examples, store [[1,2],[3,4]] into M1 and  
[[5,6],[7,8]] into M2.  
Example  
1. Create the first matrix.  
MATRIX  
1
3
2
4
*e,  
2. Create the second  
matrix.  
MATRIX *e,  
5
6
*e, 7  
8
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, use the following key presses:  
j 2  
12-6  
Matrices  
To multiply two  
matrices  
To multiply the two matrices M1 and M2 that you created for  
the previous example, use the following keystrokes:  
M1  
M2  
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 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, use the following keystrokes:  
M1 j  
M2  
To invert a matrix  
You can invert a square matrix in HOME by typing the matrix  
–1  
(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.  
Matrices  
12-7  
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 choose to create a vector in  
the M1 variable.  
MATRIX  
*e,  
2. Create the vector of the constants in the linear system.  
5
1
7
3. Return to the Matrix  
catalog. The vector you  
created is listed as M1.  
MATRIX  
4. Select the M2 variable and create a new matrix.  
*e,  
Select Real matrix  
5. Create a new matrix and enter the equation coefficients.  
2
4
1
3
*e,  
1
1
1
4
2
12-8  
Matrices  
6. Return to HOME and enter the calculation to left  
multiply the constants vector by the inverse of the  
coefficients matrix.  
M2  
–1  
x
M1  
7. Evaluate the calculation.  
The result is a vector of the  
solutions:  
x = 2  
y = 3  
z = –2  
An alternative method, is to use the RREF function. See  
“RREF” on page 12-12.  
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]).  
Matrices  
12-9  
About commands  
Matrix commands are listed in the CMDS menu (  
CMDS), in the matrix category.  
See “Matrix commands” on page 15-23 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)  
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)  
12-10  
Matrices  
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  
LU  
Least Squares. Displays the minimum norm least squares  
matrix (or vector).  
LSQ(matrix1, matrix2)  
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]].  
Matrices  
12-11  
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)  
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)  
12-12  
Matrices  
TRACE  
TRN  
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)  
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(IJ,4,4) creates a 4 × 4 matrix showing the  
numeral 1 for all elements except zeros on the diagonal. The  
logical operator returns 0 when I (the row number) and J  
(the column number) are equal, and returns 1 when they are  
not equal.  
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]].  
Matrices  
12-13  
Reduced-Row  
Echelon Form  
The following set of equations x 2y + 3z = 14  
2x + y z = – 3  
4x – 2y + 2z = 14  
1 2 3 14  
can be written as the augmented matrix  
2 1 –1 –3  
4 –2 2 14  
which can then stored as a  
3 × 4 real matrix in M1.  
You can use the RREF  
function to change this to  
reduced row echelon form,  
storing it as M2 for  
convenience.  
The reduced row echelon  
matrix gives the solution to  
the linear equation in the  
forth 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  
The final row of zeros in the  
reduced–row echelon form of  
the augmented matrix  
indicates an inconsistency.  
12-14  
Matrices  
13  
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 in MODES 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.  
Creating 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  
1. Open the List catalog.  
LIST.  
Catalog  
2. Highlight the list name  
you want to use (L1, etc.)  
and press  
to display  
the List editor.  
Lists  
13-1  
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 39G/40G or a PC. See  
“Sending and receiving aplets” on  
page 16-5 for further information.  
Receives a list from another HP 39G/  
40G or a PC. See “Sending and  
receiving aplets” on page 16-5 for  
further information.  
Clears the highlighted list.  
Clears all lists.  
CLEAR  
*e, or  
Moves to the end or the beginning of  
the catalog.  
*k,  
13-2  
Lists  
List edit keys  
When you press edit 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.  
*e, or  
Moves to the end or the beginning of  
the list.  
*k,  
Create a list in  
HOME  
1. Enter the list in 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.  
(You can omit the final  
brace when entering a  
list.)  
Lists  
13-3  
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 *k,ꢀor *e,ꢀto highlight the name of the list you  
want to edit (L1, etc.) and press  
contents.  
to display the list  
3. Press *k,ꢀor *e,ꢀto  
highlight the element you want to edit. In this example,  
edit the third element so that it has a value of 5.  
*e,*e,  
5
4. Press  
.
13-4  
Lists  
To insert an  
1. Open the List catalog.  
element in a list  
LIST.  
2. Press *k,ꢀor *e,ꢀto highlight the name of the list you  
want to edit (L1, etc.) and press  
contents.  
to display the list  
3. Press *k,ꢀor *e,ꢀto the  
insertion position.  
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.  
*e,  
9
4. Press  
.
To store one  
element  
In HOME, enter value  
to store the second element of L1 to 148, type  
148 L1(2)  
listname(element). For example,  
.
Lists  
13-5  
Deleting lists  
To delete a list  
In the List catalog, highlight the list name and press  
You are prompted if you want to delete the contents of the  
.
highlighted list variable. Press  
In the List catalog, press  
to delete the contents.  
To delete all lists  
CLEAR.  
Transmitting lists  
You can send lists to calculators or PCs just as you can aplets,  
programs, matrices, and notes.  
1. Align the HP 39G calculators’ infrared ports.  
2. Open the List catalogs on both calculators.  
3. Highlight the list to send.  
4. Press  
5. Press  
.
on the receiving calculator.  
Lists can also be transmitted to or from a computer a cable and  
Connectivity Kit.  
13-6  
Lists  
List functions  
Following are details of list functions. 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 displays  
the List category. Press *A,, select a function, and press  
.
List functions have the following syntax:  
Functions have arguments that are enclosed in  
parentheses and separated by commas. Example:  
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  
up 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.  
Lists  
13-7  
CONCAT  
Concatenates two lists into a new list.  
CONCAT(list1,list2)  
Example  
CONCAT({1,2,3},{4})returns {1,2,3,4}.  
LIST  
Creates a new list composed of 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  
1
2
n
{x x ... x x }.  
2
1
n
n–1  
LIST(list1)  
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 *A,  
Select 1LIST  
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 list of squares from 23 to 27.  
L *A,Select  
MAKELIST  
A
A
23  
27  
1
H I N T  
If the Decimal Mark setting in the Modes input form  
MODES)is set to Comma, use instead of  
(
.
13-8  
Lists  
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 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)  
Lists  
13-9  
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 90  
89 65 70 89  
}
L1  
H I N T  
If the Decimal Mark setting in the Modes input form  
(
MODES)is set to Comma, use  
instead of  
.
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 column1  
(C1).  
13-10  
Lists  
4. In the Symbolic view, define H1 (for example) as C1  
(sample) and 1 (frequency). Make sure that H1 is  
checkmarked.  
5. Go to the Numeric view  
to display calculated statistics.  
See “One-variable” on page 8-13 for the meaning of each  
computed statistic.  
Lists  
13-11  
14  
Notes and sketches  
Introduction  
The HP 39G/40G 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  
14-1  
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.  
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.  
CMDS  
Menu for entering program  
commands.  
CHARS  
Displays special characters. To type  
one, highlight it and press  
. To  
copy a character without closing the  
CHARS screen, press  
.
14-2  
Notes and sketches  
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  
view  
to exit the Sketch  
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.  
CLEAR  
Erases the entire sketch set.  
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.  
SKETCH for the Sketch view.  
and move the cursor to  
4. Move the cursor in any direction to the end point of the  
line by pressing the *k,, *e,,*A,,*>, keys.  
5. Press  
to finish the line.  
Notes and sketches  
14-3  
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  
. This turns on box-drawing.  
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  
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.  
DRAW keys  
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 by moving the  
cursor.  
Draws a box from the cursor’s starting  
position to the point at which you press  
.
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  
circle.  
to draw the  
14-4  
Notes and sketches  
To label parts of a  
sketch  
1. Press  
Alpha shift on, press  
(for lowercase).  
and type the text in the edit line. To lock the  
(for uppercase) or  
To make the label a smaller character size, turn off  
before pressing . ( is a toggle 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 *k,,  
*e,,*A,,*>, keys.  
4. Press  
5. Press  
again to affix the label.  
to continue  
drawing, or press  
to exit 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  
.
Notes and sketches  
14-5  
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 (  
graphic will be copied here.  
SKETCH). The  
2. Press  
,
. Highlight Graphic, then press *A,  
and highlight the name of the variable (G1, etc.).  
3. Press to recall the contents of the graphics  
variable.  
4. Move the box to where you would like to copy the  
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 14-8.  
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  
Note: In this example,  
the name of the note is ‘MYNOTE’.  
14-6  
Notes and sketches  
4. Write your note.  
See “Note edit keys” on  
page 14-2 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 39G/40G or PC.  
Receives a note being  
transmitted from another  
HP 39G/40G or PC.  
Deletes the selected note.  
CLEAR  
Deletes all notes in the catalog.  
Notes and sketches  
14-7  
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-hand  
list, then highlight the name “Assignments” in the right-  
hand list.  
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 column,  
then press *A, and highlight NoteTextin the right  
column.  
3. Press  
to recall the contents of the Note view  
into the note “Assignments”.  
14-8  
Notes and sketches  
15  
Programming  
Introduction  
This chapter describes how to program using the HP 39G/  
40G. 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:  
www.hp.com/calculators  
The Contents of a  
Program  
An HP 39G/40G 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.  
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.  
Programming  
15-1  
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. If  
you haven't created any programs, the only name you'll  
see is Editline.  
Editline contains 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 39G/40G runs the  
contents of Editline.)  
Editline is  
a built-in  
function.  
Program catalog menu  
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.  
15-2  
Programming  
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 39G/40G or to a disk  
drive.  
Receives the highlighted program  
from another HP 39G/40G or from a  
disk drive.  
Runs the highlighted program.  
*k, or *e,  
Moves to the beginning or end of the  
Program catalog.  
Deletes the highlighted program.  
CLEAR  
Deletes all programs in the program  
catalog.  
Programming  
15-3  
Creating and editing programs  
Create a new  
program  
1. Press  
2. Press  
PROGRM to open the Program catalog.  
.
The HP 39G/40G  
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 (" "). Dont 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.  
15-4  
Programming  
Enter  
commands  
Until you become familiar with the HP 39G/40G commands,  
the easiest way to enter commands is to use the Commands  
menu from the Program editor. You can always type in  
commands using alpha characters.  
1. From the Program editor, press  
Program Commands menu.  
CMDS to open the  
CMDS  
2. On the left, use *e,ꢀorꢀ*k,ꢀto highlight a command  
category, then pressꢀ*A, to access the commands in the  
category. Select the command that you want.  
*e,*e,*A,*e,  
3. Press  
to paste the command into the program editor.  
To enter functions (more  
to come)  
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 39G/40G 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.  
Programming  
15-5  
Editing keys  
The editing keys are:  
Key  
Meaning  
Inserts the  
point.  
character at the editing  
Inserts space into text.  
Displays previous page of the program.  
Displays next page of the program.  
Moves up or down one line.  
*k,*e,  
*A,*>,  
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.  
Menus for entering variable names,  
contents of variables, math functions,  
and program constants.  
CMDS  
Menus for entering program  
conmmands.  
CHARS  
Displays all characters. To type one,  
highlight it and press  
.
To enter several characters in a row, use  
the  
menu key while in the CHARS  
menu.  
15-6  
Programming  
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 39G/40G 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 HP 39G/40G 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. Choose  
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. Re-start the program.  
4. Repeat the process until you find and correct all errors.  
Stop a  
program  
You can stop the execution of a program at any time by  
pressing CANCEL (the  
key). Note: You may have to press  
it a couple of times.  
Programming  
15-7  
Working with programs  
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  
5. Press  
to open the Variable menu.  
to quickly scroll to Program.  
6. Press *A,, then highlight the program you want to copy.  
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).  
Delete a  
program  
You can delete any program except Editline.  
1. Press  
PROGRM to open the Program catalog.  
2. Highlight a program to delete, then press  
.
15-8  
Programming  
Delete all  
programs  
You can delete all programs at once.  
1. In the Program catalog, press  
CLEAR.  
2. Press  
.
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.  
About customizing an aplet  
You can configure 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 aplet type that you want to use, for  
example the Function aplet or the Statistics aplet. The  
copied aplet inherits all the properties of the parent aplet.  
Save the standard aplet under a new name.  
2. Configure the new aplet if you need to, for example by  
presetting axes or angle measures.  
3. Develop the programs to work with your 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 15-10.  
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 15-14 for information  
on the command.  
5. Ensure that the new aplet is selected, then run the menu  
configuration program to configure the aplet’s VIEWS  
menu.  
6. Test the aplet and debug the associated programs.(Refer  
to “Debug a program” on page 15-7).  
Programming  
15-9  
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.  
Customizing an aplet example  
This example aplet is designed to demonstrate the process of  
configuring 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.  
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 configure the angle format.  
15-10  
Programming  
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  
programs  
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.  
6. Open the Program catalog and create a program named  
“EXP.SV”. Include the following code in the program.  
(Text shown in italics below are comments only.)  
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.  
Programming  
15-11  
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 15-14.  
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.  
;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.ANG is 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.  
15-12  
Programming  
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 RUN 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  
START to run your new aplet.  
Programming  
15-13  
Programming commands  
This section describes the commands for programming with  
HP 39G/40G. You can enter these commands in your program  
by typing them or by accessing them from the Commands  
menu.  
Aplet commands  
These commands control aplets.  
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 to F3  
in Symbolic view, F3 would be plotted in Plot view, 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 “About  
customizing an aplet” on page 15-9 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 View 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.  
15-14  
Programming  
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 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.  
Programming  
15-15  
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  
autorun if the user chooses the RESET button in the APLET  
view.  
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 View 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 selected.  
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.  
15-16  
Programming  
View numbers  
The 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  
Programs Catalog  
Plot-Detail  
Plot-Table  
Overlay Plot  
Auto scale  
Decimal  
Plot  
Symbolic  
Numeric  
Plot-Setup  
Symbolic-Setup  
Numeric-Setup  
Views  
Note  
Sketch view  
Aplet Catalog  
Integer  
Trig  
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  
Example  
1&A :  
IF A==1  
THEN MSGBOX A " EQUALS 1" :  
END  
Programming  
15-17  
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  
1&A :  
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 test  
1
is true, true-clause is executed, and execution skips to END.  
1
If test-clause if false, execution proceeds to test-clause .  
1
2
Execution with the CASE structure continues until a true-  
clause is executed (or until all the test-clauses evaluate to  
false).  
IFERR...  
THEN...  
END...  
Many conditions are automatically recognized by the HP  
39G/40G as error conditions and are automatically treated as  
errors in programs.  
IFERR...THEN...END allows a program to intercept error  
conditions that otherwise would cause the program to abort.  
Its syntax is:  
IFERR trap-clause  
THEN error-clause END  
15-18  
Programming  
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 aplets Xmin, Xmax, Ymin,  
and Ymax values. The following examples assume the HP  
39G/40G default settings with the Function aplet as the  
current aplet.  
ARC  
Draws a circular arc, of given radians, whose centre is at (x,y)  
The arc is drawn from start_angle_measurement, and  
end_angle_measurement.  
ARCx;y;radius;start_angle_measurment;  
end_angle_measurment:  
Example  
ARC0;0;2;0;360:  
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 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), upperꢀ  
corner at (1,1)  
ERASE  
Clears the display  
ERASE:  
Programming  
15-19  
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;y2ꢁ  
PIXOFF  
PIXON  
TLINE  
Turns off the pixel at the specified coordinates (x,y).  
PIXOFFx;yꢁ  
Turns on the pixel at the specified coordinates (x,y).  
PIXONx;yꢁ  
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;y2ꢁ  
Example  
TLINE 0;0;3;3ꢁ  
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→  
Stores the current display in graphicname.  
DISPLAYgraphicname  
DISPLAY  
Displays graphic from graphicname in the display.  
DISPLAY graphicname  
15-20  
Programming  
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 39G/40G creates a  
graphic display like that created by the SHOWoperation.  
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  
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.  
PLOTgraphicname  
PLOTand DISPLAYcan 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 &PageNum:  
PLOTPage:  
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:  
Programming  
15-21  
REPLACE  
SUB  
Replaces portion of graphic in graphicname1 with  
graphicname2,starting at position.REPLACEalso works  
for lists and matrices.  
REPLACEgraphicname1;(position);graphicname2:  
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):  
ZEROGROB  
Creates a blank graphic with given width and height, and  
stores it in graphicname.  
ZEROGROB graphicname;width;height:  
Loop commands  
Loop structures allow a program to execute a routine  
repeatedly. The HP 39G/40G 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 structure 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 & A:  
DO A + 1 & A  
UNTIL A == 12  
END  
WHILE…  
REPEAT…  
END  
While... Repeat... Endis a loop structure 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  
1ꢀ&ꢀA:  
WHILE A < 12  
REPEAT A+1 &ꢀA  
END  
15-22  
Programming  
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  
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  
ADDROW  
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.  
ADDCOLname;[value1,...,value ];column_number  
n
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  
DELROW  
EDITMAT  
Delete Column. Deletes the specified column from the  
specified matrix.  
DELCOL name;column_number  
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  
Programming  
15-23  
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  
SCALEADD  
SUB  
Multiplies the specified row_number of the specified matrix  
by value.  
SCALEname;value;rownumber  
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  
SWAPROW  
Swaps Columns. Exchanges column1 and column2 of the  
specified matrix.  
SWAPCOL name;column1;column2  
Swap Rows. Exchanges row1and row2 in the specified  
matrix.  
SWAPROWname;row1;row2  
15-24  
Programming  
Print commands  
These commands print to an HP infrared printer, for example  
the HP 82240B printer. Note: The HP 40G does not have an  
infrared port and will not print to an infrared 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  
You can use the following commands to prompt users for  
input during your program or to provide information to users.  
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  
CHOOSEdefault_option_number; title; option ; option ;  
1
2
...option  
n
where default_option_number 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 in the  
1
n
Choose Box.  
Programming  
15-25  
Example  
3 & A:CHOOSE A;  
"COMIC STRIPS";  
"DILBERT";  
"CALVIN&HOBBES";  
"BLONDIE";  
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)  
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  
5.152000 & DATE(sets the date to May 15, 2000).  
10.1500 & TIME(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 EDITMATcommand can also be used to create matrices.  
1. Press  
2. Press  
CMDS  
*A,  
M 1, and then press  
.
3. The Matrix catalog opens with M1 available for editing.  
EDITMATmatrixname is a shortcut to opening the  
matrix editor with matrixname.  
15-26  
Programming  
FREEZE  
GETKEY  
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  
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  
INPUT  
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:  
Programming  
15-27  
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+2 becomes AREA IS:4. Use  
CHARS  
to type the quote marks " ".  
MSGBOXtextitem:  
Example  
1& A:  
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.  
PROMPT  
WAIT  
Displays an input box with name as the title, and prompts for  
a value for name. name can only be one character in length.  
PROMPTname  
Halts program execution for the specified number of seconds.  
WAITseconds  
15-28  
Programming  
Stat-One and Stat-Two commands  
The following commands are used for analysis of 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  
define at least two data points.  
DO1VSTATSdatasetname  
SETFREQ  
Defines 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  
Defines 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. Datasetname  
can be SI, S2,..., or S5. Datasetname must define at least four  
pairs of data points.  
DO2VSTATSdatasetname  
SETDEPEND  
SETINDEP  
Defines datasetname dependent column. Datasetname can be  
S1, S2, …, or S5 and column can be C0–C9.  
SETDEPENDdatasetname;column  
Defines datasetname independent column. Datasetname can  
be S1, S2,…, or S5 and column can be C0–C9.  
SETINDEPdatasetname;column  
Programming  
15-29  
Storing and retrieving variables in programs  
The HP 39G/40G has both Home variables and Aplet  
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 11-4. 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.  
Plot-view variables  
The following aplet variables control the Plot view.  
Area  
)XQFWLRQ  
Contains the last value found by the Area function in Plot-  
FCN menu.  
Axes  
Turns axes on or off.  
$OOꢀ$SOHWV  
From Plot Setup, check (or uncheck) AXES.  
or  
In a program, type:  
1 & Axes—to turn axes on (default).  
0 & Axes—to turn axes off.  
Connect  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
Draws lines between successively plotted points.  
From Plot Setup, check (or uncheck) CONNECT.  
or  
6ROYH  
6WDWLVWLFV  
In a program, type  
1 & Connect—to connect plotted points (default,  
except in Statistics where the default is off).  
0 & Connect—not to connect plotted points.  
15-30  
Programming  
Coord  
Turns the coordinate-display mode in Plot view on or off.  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
6HTXHQFH  
6ROYH  
From Plot view, use the Menu mean key to toggle coordinate  
display on an off.  
In a program, type  
1 &ꢀCoord—to turn coordinate display on (default).  
6WDWLVWLFV  
0 &ꢀCoord—to turn coordinate display off.  
Extremum  
)XQFWLRQ  
Contains the last value found by the Extremum operation in  
the Plot-FCN menu.  
FastRes  
)XQFWLRQ  
6ROYH  
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 &ꢀFastRes—for faster (default).  
0 &ꢀFastRes—for more detail.  
Grid  
$OOꢀ$SOHWV  
Turns the background grid in Plot view on or off. From Plot  
setup, check (or uncheck) GRID.  
or  
In a program, type  
1 &ꢀGridto turn the grid on.  
0 & Gridto turn the grid off (default).  
Hmin/Hmax  
Defines minimum and maximum values for histogram bars.  
6WDWLVWLFV  
From Plot Setup for one-variable statistics, set values for  
HRNG.  
or  
In a program, type  
n1 ꢀ& Hmin  
n2 & Hmax  
where n2 > n1  
Programming  
15-31  
Hwidth  
Sets the width of histogram bars.  
6WDWLVWLFV  
From Plot Setup in 1VAR stats set a value for Hwidth  
or  
In a program, type  
n& Hwidth  
Indep  
$OOꢀ$SOHWV  
Defines the value of the independent variable used in tracing  
mode.  
In a program, type  
n& Indep  
InvCross  
$OOꢀ$SOHWV  
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 & InvCross—to invert the crosshairs.  
0 & InvCross—for solid crosshairs (default).  
Isect  
)XQFWLRQ  
Contains the last value found by the Intersection function in  
the Plot-FCN menu.  
Labels  
Draws labels in Plot view showing X and Y ranges.  
$OOꢀ$SOHWV  
From Plot Setup, check (or uncheck) Labels  
or  
In a program, type  
1 &Labels—to turn labels on.  
0 &Labels—to turn labels off (default).  
15-32  
Programming  
Nmin / Nmax  
6HTXHQFH  
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 &Nmin  
n2 &Nmax  
where n2 > n1  
Recenter  
Recenters at the crosshairs locations when zooming.  
$OOꢀ$SOHWV  
From Plot-Zoom-Set Factors, check (or uncheck)  
Recenter  
or  
In a program, type  
1 & Recenter— to turn recenter on (default).  
0 & Recenter—to turn recenter off.  
Root  
)XQFWLRQ  
Contains the last value found by the Rootfunction in the  
Plot-FCN menu.  
S1mark–S5mark  
Defines the mark to use for statistics 2-variable scatter plots.  
6WDWLVWLFV  
From Plot Setup for two-variable statistics, S1mark-  
S5mark, then choose a mark.  
or  
In a program, type  
n & S1mark  
where n is 1,2,3,...5  
SeqPlot  
Toggles type of sequence plot: Stairstep or Cobweb.  
6HTXHQFH  
From Plot Setup, select SeqPlot, then choose Stairstep  
or Cobweb.  
or  
In a program, type  
1 &ꢀSeqPlot—for stairstep.  
2&ꢀSeqPlot—for cobweb.  
15-33  
Programming  
Simult  
Toggles between simultaneous and sequential graphing of all  
selected expressions.  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
From Plot Setup, check (or uncheck) _SIMULT  
or  
6HTXHQFH  
In a program, type  
1 & Simult—for simultaneous graphing.  
0 & Simult—for sequential graphing.  
Slope  
)XQFWLRQ  
Contains the last value found by the Slope function in the  
Plot–FCN menu.  
StatPlot  
6WDWLVWLFV  
Toggles type 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  
1&ꢀStatPlot—for Histogram.  
2&ꢀStatPlot—for BoxWhisker.  
Umin/Umax  
3RODU  
Defines 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 & Umin  
n2 & Umax  
where n2 > n1  
Ustep  
Defines the step size for an independent variable.  
3RODU  
From the Plot Setup input form, enter values for USTEP.  
or  
In a program, type  
n & Ustep  
where n > 0  
15-34  
Programming  
Tmin / Tmax  
3DUDPHWULF  
Defines 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 &ꢀTmin  
n2 &ꢀTmax  
where n2 > n1  
Tracing  
$OOꢀ$SOHWV  
Turns tracing mode on or off in Plot view.  
In a program, type  
1 & Tracing—to turn Tracing mode on (default).  
0 & Tracing—to turn Tracing mode off.  
Tstep  
Defines the step size for an independent variable.  
3DUDPHWULF  
From the Plot Setup input form, enter values for TSTEP.  
or  
In a program, type  
n & Tstep  
where n > 0  
Xcross  
$OOꢀ$SOHWV  
Defines the horizontal coordinate of crosshairs. Only works  
with TRACEoff.  
In a program, type  
n & Xcross  
Ycross  
$OOꢀ$SOHWV  
Defines the vertical coordinate of crosshairs. Only works with  
TRACEoff.  
In a program, type  
n & Ycross  
Programming  
15-35  
Xtick  
$OOꢀ$SOHWV  
Defines 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 & Xtick where n > 0  
Ytick  
Defines the distance between tick marks for the vertical axis.  
$OOꢀ$SOHWV  
From the Plot Setup input form, enter a value for Ytick.  
or  
In a program, type  
n & Ytick where n > 0  
Xmin / Xmax  
$OOꢀ$SOHWV  
Defines 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  
n1 & Xmin  
n2 & Xmax  
where n2 > n1  
Ymin / Ymax  
$OOꢀ$SOHWV  
Defines 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 & Ymin  
n2 & Ymax  
where n2 > n1  
15-36  
Programming  
Xzoom  
Sets the horizontal zoom factor.  
$OOꢀ$SOHWV  
From Plot-ZOOM-Set Factors, enter the value for XZOOM.  
or  
In a program, type  
n & XZOOM  
where n > 0  
Yzoom  
Sets the vertical zoom factor.  
$OOꢀ$SOHWV  
From Plot-ZOOM-Set Factors, enter the value for YZOOM.  
or  
In a program, type  
n & YZOOM  
Symbolic-view variables  
The following aplet variables available in the Symbolic view.  
Angle  
Sets the angle mode.  
$OOꢀ$SOHWV  
From Symbolic Setup, choose Degrees, Radians, or  
Gradsfor angle measure.  
or  
In a program, type  
1 &ꢀAngle—for Degrees.  
2 &ꢀAngle—for Radians.  
3 &ꢀAngle—for Grads.  
F1...F9, F0  
)XQFWLRQ  
Can contain any expression. Independent variable is X.  
Example  
’SIN(X)’ & F1(X)  
In the above example, you must put single quotes around the  
expression to keep it from being evaluated before it is stored.  
Use  
CHARS to type the single quote mark.  
Programming  
15-37  
X1, Y1...X9,Y9  
X0,Y0  
3DUDPHWULF  
Can contain any expression. Independent variable is T.  
Example  
’SIN(4*T)’ & Y1(T):’2*SIN(6*T)’ STO&  
X1(T)  
R1...R9, R0  
3RODU  
Can contain any expression. Independent variable is θ.  
Example  
’2*SIN(2*θ)’ & R1(θ)  
U1...U9, U0  
6HTXHQFH  
Can contain any expression. Independent variable is N.  
Example  
RECURSE (U,U(N-1)*N,1,2) & U1(N)  
E1...E9, E0  
6ROYH  
Can contain any equation or expression. Independent variable  
is selected by highlighting it in Numeric View.  
Example  
’X+Y*X-2=Y’ & E1  
S1fit...S5fit  
6WDWLVWLFV  
Defines 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 names or  
numbers into a variable S1fit, S2fit, etc.  
1. Linear  
2. LogFit  
3. ExpFit  
4. Power  
5. QuadFit  
6. Cubic  
7. Logist  
8. Userdefined  
Example  
Cubic & S2fit  
or  
6 & S2fit  
15-38  
Programming  
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  
C0through C9, for columns of data. Can contain lists.  
6WDWLVWLFV  
Enter data in the Numeric view  
or  
In a program, type  
LIST&Cn  
where n = 0, 1, 2, 3 ... 9  
Digits  
Number of decimal places to use for Number format.  
$OOꢀ$SOHWV  
From Solves Numeric Setup view, enter a value in the second  
field of Number Format.  
or  
In a program, type  
n & Digits  
where 0 <n <11  
Except in Solve, the value of Digitstakes effect only after  
the current aplet is saved with a new name. Until then,  
HDigitis in effect.  
Programming  
15-39  
Format  
Defines the number display format.  
$OOꢀ$SOHWV  
From Solves Numeric Setup view, choose Standard,  
Fixed, Scientific, or Engineeringin the Number  
Formatfield.  
or  
In a program, store the constant name (or its number) into the  
variable Format.  
1. Standard  
2. Fixed  
3. Scientific  
4. Engineering  
Note: Fraction is not a valid mode in aplets.  
Except in Solve, the value of Format takes effect only after the  
current aplet is saved with a new name. Until then, HFormat  
is in effect.  
Example  
Scientific& Format  
or  
3 & Format  
NumCol  
$OOꢀ$SOHWVꢀH[FHSWꢀ  
6WDWLVWLFVꢀDSOHW  
Defines the highlighted column in Numeric view.  
In a program, type  
n & NumCol  
where n can be 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.  
NumFont  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
Toggles the font size in Numeric view. Does not appear in the  
Num Setup input form. Corresponds to the BIG key in  
Numeric view.  
In a program, type  
6HTXHQFH  
6WDWLVWLFV  
0 & NumFontfor small (default).  
1 & NumFontfor big.  
NumIndep  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
List of independent values used by Build Your Own Table.  
In a program, type  
LIST& NumIndep  
6HTXHQFH  
15-40  
Programming  
NumRow  
$OOꢀ$SOHWVꢀH[FHSWꢀ  
6WDWLVWLFVꢀDSOHW  
Defines the highlighted row in Numeric view.  
In a program, type  
n & NumRow  
where n > 0  
NumStart  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
Defines the starting value for a table in Numeric view.  
From Num Setup, enter a value for NUMSTART.  
or  
6HTXHQFH  
In a program, type  
n & NumStart  
NumStep  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
Defines the step size (increment value) for an independent  
variable in Numeric view.  
From Num Setup, enter a value for NUMSTEP.  
or  
6HTXHQFH  
In a program, type  
n & NumStep  
where n > 0  
NumType  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
Choose a table format.  
From Num Setup, choose Automaticor BuildYour  
Own.  
or  
6HTXHQFH  
In a program, type  
0 & NumTypefor Build Your Own.  
1 & NumTypefor Automatic (default).  
NumZoom  
)XQFWLRQ  
3DUDPHWULF  
3RODU  
Defines the Zoom factor in the Numeric view.  
From Num Setup, type in a value for NUMZOOM.  
or  
6HTXHQFH  
In a program, type  
n & NumZoom  
where n > 0  
Programming  
15-41  
StatMode  
6WDWLVWLFV  
Toggles between 1–variable and 2–variable statistics in the  
Statistics aplet. Does not appear in the Plot Setup input form.  
Corresponds to the  
View.  
and  
menu keys in Numeric  
In a program, store the constant name (or its number) into the  
variable StatMode. 1VAR=1, 2VAR=2.  
Example  
1VAR & StatMode  
or  
1 & StatMode  
Note variables  
The following aplet variable is available in Note view.  
NoteText  
Use NoteText to recall text previously entered in Note view.  
$OOꢀ$SOHWV  
Sketch variables  
The following aplet variables are available in Sketch view.  
Page  
$OOꢀ$SOHWV  
Defines a page in a sketch set. A sketch set can contain up to  
10 graphics. 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 & Page  
PageNum  
$OOꢀ$SOHWV  
Index for referring to a particular page of the sketch set (in  
Sketch view).  
In a program, type the page that is shown when  
is pressed.  
SKETCH  
n & PageNum  
15-42  
Programming  
16  
Extending aplets  
Aplets are the application environments where you explore  
different classes of mathematical operations.  
You can extend the capability of the HP 39G/40G 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 39G calculators via an infra  
red link.  
Download e-lessons (teaching aplets) from the Hewlett-  
Packard’s Calculator web site.  
Program new aplets. See chapter 15, 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. You can send your aplet to other  
calculators so that other people can use it.  
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.  
Extending aplets  
16-1  
Aplet Keys  
Key  
Meaning  
Saves the highlighted aplet with a name.  
Resets the default values and settings in  
the highlighted aplet. This erases any  
stored data or functions.  
Alphabetically or chronologically sorts  
the items in the Aplet Library menu list.  
Transmits the highlighted aplet to  
another HP 39G/40G or a storage  
device.  
Receives the aplet sent from another  
HP 39G/40G or storage device.  
(receive)  
(or  
Opens the selected aplet.  
)
Example: To create  
a new aplet from an  
existing Solve aplet  
A simple example of a customized aplet is the TRIANGLES  
aplet. This aplet is a copy of the Solve aplet containing the  
formulas commonly used in calculations involving  
right–angled triangles.  
1. In APLET, highlight Solveand SAVE it under the new  
name.  
Select Solve  
T R I A N G L E S  
2. Enter the four formulas:  
θ
O
j
H
θ
θ
A j  
H
O j  
A
A
B
C
16-2  
Extending aplets  
3. Decide whether you want the aplet to operate in Degrees,  
Radians, or Grads.  
MODES  
Select Degrees  
4. Ensure the TRIANGLES aplet is saved in the Aplet  
Library.  
The Solve aplet can now  
be reset and used for other  
problems.  
Example: To use  
the customized  
aplet  
To use the 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 if it  
o
forms an angle of 35 with the horizontal and extends 5 metres  
up the wall.  
1. Select the aplet.  
Select  
TRIANGLES  
2. Choose the sine formula in  
E1.  
*k,*k,*k,*k,ꢀ  
3. Change to the Numeric  
view and enter the known  
values.  
35  
5
Extending aplets  
16-3  
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.  
Annotating an aplet with notes  
The Note view (  
NOTE) attaches a note to the current  
aplet. See Chapter 14, “Notes and Sketches.”  
Annotating an aplet with sketches  
The Sketch view (  
SKETCH) attaches a picture to the  
current aplet. See chapter 14, “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:  
www.hp.com/calculators  
16-4  
Extending aplets  
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 39G to another. This takes place via the infrared port.  
You can also send aplets to, and receive aplets from, a remote  
storage device (aplet disk drive or computer). This takes place  
via a cable connection and requires an aplet disk drive or  
special software running on a PC (such as the PC Connectivity  
Kit). Note: The HP 40G does not have an IR port. A PC  
adapter and unit–to–unit cable is supplied instead.  
To transmit an  
aplet  
1. Connect the storage device 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 2 inches (5 cm) apart.  
2. Sending calculator: Open the Library, highlight the aplet  
to send, and press  
.
You have two options: another HP 39G or a disk  
drive on a PC. 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  
.
You have two options: another HP 39G or a disk  
drive (or computer). 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.  
Extending aplets  
16-5  
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  
press  
. Select the sorting scheme and  
.
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, andess  
aplets, press  
. To delete all custom  
CLEAR.  
16-6  
Extending aplets  
R
Reference information  
Regulatory information  
This section contains information that shows how the  
HP 39G/40G graphing calculator complies with regulations in  
certain regions. Any modifications to the calculator not  
expressly approved by Hewlett-Packard could void the  
authority to operate the HP 39G/40G in these regions.  
USA  
This calculator generates, uses, and can radiate radio  
frequency energy and may interfere with radio and television  
reception. The calculator complies 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.  
However, there is no guarantee that interference will not occur  
in a particular installation. In the unlikely event that there is  
interference to radio or television reception (which can be  
determined by turning the calculator 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.  
Relocate the calculator, with respect to the receiver.  
Connections to  
peripheral  
devices  
To maintain compliance with FCC Rules and Regulations, use  
only the cable accessories provided.  
Canada  
This Class B digital apparatus complies with Canadian EMC  
Class B requirements.  
Cet appareil numérique de la classe B est comforme à la classe  
B des normes canadiennes de compatibilité  
électromagnétiques (CEM).  
Reference information  
R-1  
LED safety  
The infrared port located on the top of the calculator is  
classified as a Class 1 LED (light emitting diode) device  
according to International Standard IEC 825-1 (EN 60825-1.  
This device is not considered harmful, but the following  
precautions are recommended:  
Do not attempt to make any adjustments to the unit.  
Avoid direct eye exposure to the infrared LED beam. Be  
aware that the beam is invisible light and cannot be seen.  
Do not attempt to view the infrared LED beam with any  
type of optical device.  
CLASS 1 LED PRODUCT  
LEDSCHÜTZKLASSE 1 PRODUKT  
Warranty  
HP 39G/40G Graphical 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.  
R-2  
Reference information  
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.  
4. HP products may contain re manufactured 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.  
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 exclusion might not apply to you. This warranty gives  
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  
YOUR SOLE AND EXCLUSIVE REMEDIES.  
EXCEPT AS INDICATED ABOVE, IN NO EVENT  
WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS  
OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL,  
CONSEQUENTIAL (INCLUDING LOST PROFIT OR  
DATA), OR OTHER DAMAGE, WHETHER BASED  
IN CONTRACT, TORT, OR OTHERWISE. Some  
countries, States or provinces do not allow the exclusion  
or limitation of incidental or consequential damages, so  
the above limitation or exclusion may not apply to you.  
Reference information  
R-3  
8. 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.  
CAS  
The HP 40G is packaged with a computerized algebra system  
(CAS). Refer to the CAS User Manual for further  
information.  
Resetting the HP 39G/40G  
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 below, “To erase all memory and reset defaults”.  
To reset using  
the keyboard  
Press and hold the  
simultaneously, then release them.  
key and the third menu key  
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.  
R-4  
Reference information  
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.  
Note: To cancel this process, release only the top-row  
keys, then press the third menu key.  
If the calculator does not turn on  
If the HP 39G/40G 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-7), press  
and hold the key for 10 seconds, and then put the  
batteries back in. Press the key.  
key.  
Reference information  
R-5  
Glossary  
aplet  
A small application, limited to one  
topic. The built-in aplet types are  
Function, Parametric, Polar, Sequence,  
Solve, and Statistics. 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 DISPexpression;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  
The basic starting point of the  
calculator. Go to HOME to do  
calculations.  
Library  
list  
For aplet management: to start, save,  
reset, send and receive aplets.  
A set of values separated by commas  
(periods if the Decimal Mark is 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 is 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.  
R-6  
Reference information  
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  
variable  
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.  
The name of a number, list, matrix, note,  
or graphic that is stored in memory. Use  
to store and use  
to retrieve.  
vector  
A one-dimensional array of values  
separated by commas (periods if the  
Decimal Mark is Comma) and enclosed  
in single brackets. Created and  
manipulated by the Matrix catalog and  
editor.  
views  
The possible contexts for an aplet: Plot,  
Plot Setup, Numeric, Numeric Setup,  
Symbolic, Symbolic Setup, Sketch,  
Note, and special views like split  
screens.  
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 4.5V dc, 60mA maximum.  
Batteries  
When battery power is low, the (()) annunciator stays on,  
even when the calculator is off. There is also a warning  
Reference information  
R-7  
message that appears when the calculator is on:  
Warning: Low Bat.  
The HP 39G/40G uses three AAA batteries. Be sure all three  
are of the same brand and type. Rechargeable batteries are not  
recommended because of their lower capacity and more  
sudden demise.  
To replace batteries:  
1. Turn the calculator off and place the slide cover over the  
keyboard to prevent keys from being pressed.  
CAUTION  
Your calculator can lose memory if it is turned on while the  
batteries are being removed.  
Under no circumstances should the batteries be deliberately  
inserted backwards and the calculator turned on. This may  
cause hardware damage and will void the warranty.  
2. Remove the battery compartment door from the rear of  
the calculator by pressing down on the dimple and  
pushing the door off.  
3. Replace the batteries within 2 minutes to avoid memory  
loss. Position the fresh batteries according to the diagram  
inside the battery compartment.  
The Netherlands  
This regulation applies only to The Netherlands.  
Batteries are delivered with this  
product. When empty do not throw  
them away but collect as small  
chemical waste.  
Bij dit produkt zijn batterijen  
geleverd. Wanneer deze leeg zijn,  
moet u ze niet weggoolen maar  
inlevern als KCA.  
Menu maps of the VARS menu  
Home variables  
The home variables are:  
Category  
Available name  
Complex  
Z1...Z9, Z0  
R-8  
Reference information  
Category  
Graphic  
Library  
Available name (Continued)  
G1...G9, G0  
Function  
Parametric  
Polar  
Sequence  
Solve  
Statistics  
User-named  
List  
L1...L9, L0  
Matrix  
Modes  
M1...M9, M0  
Ans  
Date  
HAngle  
HDigits  
HFormat  
Ierr  
Time  
Notepad  
Program  
User-named  
Editline  
User-named  
Real  
A...Z, θ  
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  
Reference information  
R-9  
Category  
Available name (Continued)  
Plot-FCN  
Area  
Extremum  
Isect  
Root  
Slope  
Symbolic  
Numeric  
Angle  
F1  
F6  
F7  
F8  
F9  
F0  
F2  
F3  
F4  
F5  
Digits  
Format  
NumCol  
NumFont  
NumIndep  
NumRow  
NumStart  
NumStep  
NumType  
NumZoom  
Note  
NoteText  
Page  
Sketch  
PageNum  
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  
R-10  
Reference information  
Category  
Available name (Continued)  
Symbolic  
Angle  
X1  
Y5  
X6  
Y6  
X7  
Y7  
X8  
Y8  
X9  
Y9  
X0  
Y0  
Y1  
X2  
Y2  
X3  
Y3  
X4  
Y4  
X5  
Numeric  
Digits  
Format  
NumCol  
NumFont  
NumIndep  
NumRow  
NumStart  
NumStep  
NumType  
NumZoom  
Note  
NoteText  
Page  
Sketch  
PageNum  
Polar aplet variables  
The polar aplet variables are:  
Category  
Available names  
Axes  
Connect  
Coord  
Xcross  
Ycross  
Xtick  
Ytick  
Xmin  
Grid  
Indep  
InvCross  
Labels  
Recenter  
Simult  
Umin  
Xmax  
Ymin  
Ymax  
Xzoom  
Yxoom  
Umax  
θstep  
Tracing  
Symbolic  
Angle  
R1  
R6  
R7  
R8  
R9  
R0  
R2  
R3  
R4  
R5  
Reference information  
R-11  
Category  
Available names (Continued)  
Numeric  
Digits  
Format  
NumCol  
NumFont  
NumIndep  
NumRow  
NumStart  
NumStep  
NumType  
NumZoom  
Note  
NoteText  
Page  
Sketch  
PageNum  
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-12  
Reference information  
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  
Reference information  
R-13  
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-14  
Reference information  
Menu maps of the MATH menu  
Math functions  
The math functions are:  
Category  
Available name  
Calculus  
%
)
TAYLOR  
Complex  
Constant  
ARG  
IM  
RE  
CONJ  
e
i
MAXREAL  
MINREAL  
π
Hyperb.  
List  
ACOSH  
ASINH  
ATANH  
COSH  
TANH  
ALOG  
EXP  
EXPM1  
LNP1  
SINH  
CONCAT  
LIST  
MAKELIST  
πLIST  
POS  
REVERSE  
SIZE  
ΣLIST  
SORT  
Loop  
ITERATE  
RECURSE  
Σ
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  
Reference information  
R-15  
Category  
Available name (Continued)  
Polynom.  
POLYCOEF  
POLYEVAL  
POLYFORM  
POLYROOT  
Prob.  
Real  
COMB  
!
PERM  
RANDOM  
UTPC  
UTPF  
UTPN  
UTPT  
CEILING  
DEGRAD  
FLOOR  
FNROOT  
FRAC  
HMS→  
HMS  
INT  
MIN  
MOD  
%
%CHANGE  
%TOTAL  
RADDEG  
ROUND  
SIGN  
MANT  
MAX  
TRUNCATE  
XPON  
Stat-Two  
Symbolic  
PREDX  
PREDY  
=
QUAD  
QUOTE  
|
ISOLATE  
LINEAR?  
Tests  
AND  
IFTE  
NOT  
OR  
<
= =  
XOR  
>
Trig  
ACOT  
ACSC  
ASEC  
COT  
CSC  
SEC  
R-16  
Reference information  
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  
StatMode  
StatPlot  
Stat1Var  
Stat2Var  
Hist  
BoxW  
Reference information  
R-17  
Program commands  
The program commands are:  
Category  
Command  
Aplet  
CHECK  
SELECT  
SETVIEWS  
UNCHECK  
Branch  
IF  
CASE  
IFERR  
RUN  
THEN  
ELSE  
END  
STOP  
Drawing  
Graphic  
ARC  
LINE  
BOX  
PIXOFF  
PIXON  
TLINE  
ERASE  
FREEZE  
DISPLAYR  
RDISPLAY  
RGROB  
GROBNOT  
GROBOR  
GROBXOR  
MAKEGROB  
PLOTR  
RPLOT  
REPLACE  
SUB  
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  
GETKEY  
INPUT  
MSGBOX  
PROMPT  
WAIT  
CHOOSE  
DISP  
DISPTIME  
EDITMAT  
FREEZE  
Stat-One  
Stat-Two  
DO1VSTATS  
RANDSEED  
SETFREQ  
SETSAMPLE  
DO2VSTATS  
SETDEPEND  
SETINDEP  
R-18  
Reference information  
Selected status messages  
The status messages are:  
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.  
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.  
Reference information  
R-19  
Message  
Meaning (Continued)  
(OFF SCREEN)  
Function value, root, extremum,  
or intersection is not visible in the  
current screen.  
Receive Error  
Problem with data reception from  
another calculator. Re-send the  
data.  
Too Few  
Arguments  
The command requires more  
arguments than you supplied.  
Undefined Name  
The global variable named does  
not exist.  
Undefined Result  
The calculation has a  
mathematically undefined result  
(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-20  
Reference information  
Index  
aplet views  
canceling operations in 1-1  
A
absolute value 10-6  
add 10-4  
changing 1-17  
note 1-16  
Numeric view 1-15  
Plot view 1-15  
sketch 1-17  
algebraic entry 1-18  
alpha characters  
typing 1-6  
alphabetical sorting 16-6  
angle measure 1-9  
in statistics 8-10  
setting 1-11  
split-screen 1-16  
Symbolic view 1-15  
arc cosecant 10-21  
arc cosine 10-5  
arc cotangent 10-21  
arc secant 10-21  
arc sine 10-5  
arc tangent 10-5  
area  
graphical 3-10  
interactive 3-10  
variable 15-30  
arguments  
with matrices 12-10  
attaching  
a note to an aplet 14-1  
a sketch to an aplet 14-3  
auto scale 2-14  
axes  
animation 14-5  
creating 14-5  
annunciators 1-3  
Ans (last answer) 1-22  
antilogarithm 10-4, 10-10  
aplet  
attaching notes 16-4  
clearing 16-4  
copying 16-5  
definition of R-6  
deleting 16-6  
Function 10-22  
Inference 9-2  
key 1-4  
library 16-6  
Note view 14-1  
opening 1-15  
Parametric 4-1  
Polar 5-1  
plotting 2-6  
variable 15-30  
B
receiving 16-5  
resetting 16-4  
sending 16-5  
Sketch view 14-1  
Solve 7-1  
bad argument R-19  
bad guesses error message 7-7  
batteries  
changing R-8  
sorting 16-6  
statistics 8-1  
low-battery warning R-8  
box-and-whisker plot 8-16  
branch commands  
aplet commands  
CHECK 15-14  
SELECT 15-14  
SETVIEWS 15-17  
UNCHECK 15-17  
aplet variables  
definition 11-1, 11-8  
in Plot view 15-30  
new 11-1  
CASE...END 15-18  
IF...THEN...ELSE...END 15-18  
IFERR...THEN...ELSE 15-18  
RUN 15-19  
STOP 15-19  
branch structures 15-17  
build your own table 2-19  
Index  
I-1  
connectivity kit 16-5  
constant? error message 7-7  
constants 10-9  
e 10-9  
C
calculus  
operations 10-8  
catalogs 1-28  
i 10-9  
chronological sorting 16-6  
circle drawing 14-4  
clearing  
maximum real number 10-9  
minimum real number 10-9  
program R-17  
aplet 16-4  
characters 1-21  
display 1-21  
display history 1-24  
edit line 1-21  
contrast  
decreasing display 1-2  
increasing display 1-2  
coordinate display 2-8  
copying  
lists 13-6  
plot 2-6  
display 1-21  
graphics 14-6  
notes 14-8  
programs 15-8  
cobweb graph 6-2  
coefficients  
polynomial 10-12  
columns  
changing position 15-24  
combinations 10-13  
comma mode  
correlation  
coefficient 8-17  
CORR 8-17  
statistical 8-14  
cosecant 10-21  
cosine 10-4  
inverse hyperbolic 10-9  
cotangent 10-21  
covariance  
statistical 8-14  
creating  
with matrices 13-7  
commands  
aplet 15-14  
Branch 15-17  
definition of R-6  
Drawing 15-19  
Graphic 15-20  
Loop 15-22  
aplet 16-1  
notes in Notepad 14-6  
programs 15-4  
sketches 14-3  
Print 15-25  
Program 15-5, R-18  
Prompt 15-25  
critical value(s) displayed 9-4  
cross product  
vector 12-10  
curve fitting 8-11, 8-17  
Stat-One 15-29  
Stat-Two 15-29  
with matrices 12-10  
complex functions 10-6, 10-18  
complex number functions  
conjugate 10-8  
imaginary part 10-8  
real part 10-8  
D
data set definition 8-7  
date, setting 15-26  
complex numbers 1-27  
debugging programs 15-7  
decimal  
entering 1-27  
maths functions 10-8  
storing 1-28  
changing marker format 1-10  
scaling 2-14, 2-16  
confidence intervals 9-16  
conjugate 10-8  
connecting  
decreasing display contrast 1-2  
definite integral 10-7  
data points 8-18  
variable 15-30  
I-2  
Index  
deleting  
aplet 16-6  
E
e 10-9  
edit line 1-2  
editing  
lists 13-6  
matrices 12-4  
programs 15-9  
statistical data 8-10  
delimiters, programming 15-1  
derivatives  
definition of 10-7  
in Function aplet 10-24  
in Home 10-23  
determinant  
matrices 12-4  
notes 14-2  
programs 15-5  
Editline  
Program catalog 15-2  
editors 1-28  
eigenvalues 12-11  
eigenvectors 12-11  
element  
square matrix 12-10  
differentiation 10-7  
display 15-20  
storing 12-5  
E-lessons 1-11  
engineering number format 1-10  
equals  
for equations 10-19  
logical test 10-20  
equations  
adjusting contrast 1-2  
annunciator line 1-2  
capture 15-20  
clearing 1-2  
date and time 15-26  
element 12-5  
engineering 1-10  
fixed 1-10  
fraction 1-10  
history 1-21  
solving 7-1  
erasing a line in Sketch view 15-20  
error messages  
bad guesses 7-7  
constant? 7-7  
line 1-21  
list elements 13-4  
matrices 12-5  
parts of 1-2  
printing contents 15-25  
rescaling 2-14  
scientific 1-10  
scrolling through history 1-23  
soft key labels 1-2  
standard 1-10  
exclusive OR 10-21  
executing programs 15-7  
exiting views 1-17  
exponent  
minus 1 10-10  
of value 10-18  
raising to 10-6  
expression  
defining 2-1, R-6  
entering in HOME 1-18  
evaluating in aplets 2-3  
literal 10-20  
divide 10-4  
drawing  
circles 14-4  
keys 14-4  
lines and boxes 14-3  
Drawing commands  
ARC 15-19  
plot 3-3  
extremum  
interactive 3-9  
BOX 15-19  
F
ERASE 15-19  
FREEZE 15-20  
LINE 15-20  
PIXOFF 15-20  
PIXON 15-20  
factorial 10-13  
FastRes variable 15-31  
fit  
a curve to 2VAR data 8-17  
choosing 8-11  
defining your own 8-12  
regression curve 1-29  
TLINE 15-20  
Index  
I-3  
fixed number format 1-10  
font size  
one-variable statistics 8-18  
overlaying 2-16  
scatter 8-15, 8-16  
split-screen view 2-15  
splitting into plot and close-up 2-14  
splitting into plot and table 2-14  
stairsteps 6-2  
statistical data 8-15  
t values 2-5  
change 3-8, 14-5  
forecasting 8-21  
fraction number format 1-10  
full-precision display 1-10  
function  
analyse graph with FCN tools 3-3  
definition 2-2  
definition of R-6  
entering 1-18  
tickmarks 2-6  
tracing 2-8  
Graphic commands  
gamma 10-13  
DISPLAY 15-20  
GROB 15-21  
GROBNOT 15-21  
GROBOR 15-21  
GROBXOR 15-21  
MAKEGROB 15-21  
PLOT 15-21  
REPLACE 15-22  
SUB 15-22  
ZEROGROB 15-22  
intersection point 3-4  
math menu R-15  
quadratic 3-4  
slope 3-5  
syntax 10-3  
tracing 2-8  
Function aplet 2-21, 3-1  
function variables  
Area 15-30  
Axes 15-30  
graphics  
Connect 15-30  
FastRes 15-31  
Grid 15-31  
in menu map R-9  
Indep 15-32  
copying 14-6  
copying into Sketch view 14-6  
storing and recalling 14-6, 15-20  
guarantee R-2  
Isect 15-32  
Labels 15-33  
H
histogram 8-15  
Recenter 15-33  
Root 15-33  
Ycross 15-36  
adjusting 8-15  
range 8-18  
setting min/max values for bars  
15-31  
width 8-18  
G
glossary R-6  
history 1-2, 15-25  
Home 1-1  
graph  
analyzing statistical data in 8-20  
auto scale 2-14  
box-and-whisker 8-16  
capture current display 15-20  
cobweb 6-2  
calculating in 1-18  
display 1-2  
evaluating expressions 2-3  
reusing lines 1-21  
home variables 11-1, R-8  
definition 11-7  
comparing 2-5  
connected points 8-16  
defining the independent variable  
15-35  
horizontal zoom 15-37  
hyperbolic  
maths functions 10-10  
drawing axes 2-6  
expressions 3-3  
grid points 2-6  
in Solve aplet 7-8  
index values 2-6  
I-4  
Index  
hyperbolic trigonometry  
ACOSH 10-9  
ALOG 10-10  
ASINH 10-9  
ATANH 10-9  
COSH 10-9  
setting Modes 1-11  
insufficient memory R-19  
insufficient statistics data R-19  
integer rank  
matrix 12-12  
integer scaling 2-14, 2-16  
integral  
definite 10-7  
indefinite 10-25  
integration 10-7  
interpreting  
intermediate guesses 7-7  
intersection  
interactive 3-10  
invalid  
EXP 10-10  
EXPM1 10-10  
LNP1 10-10  
SINH 10-9  
TANH 10-9  
hypothesis  
alternative 9-3  
inference tests 9-9  
null 9-3  
tests 9-3  
dimension R-19  
statistics data R-19  
syntax R-19  
I
i 10-9  
inverse hyperbolic cosine 10-9  
inverse hyperbolic functions 10-10  
inverse hyperbolic sine 10-9  
inverse hyperbolic tangent 10-9  
inverting matrices 12-7  
isect variable 15-32  
implied multiplication 1-19  
importing  
graphics 14-6  
notes 14-8  
increasing display contrast 1-2  
indefinite integral  
using symbolic variables 10-25  
independent values  
K
keyboard  
adding to table 2-19  
editing keys 1-5  
entry keys 1-5  
inactive keys 1-7  
list keys 13-2  
math functions 1-7  
menu keys 1-4  
Notepad keys 14-8  
shifted keystrokes 1-6  
independent variable  
defined for Tracing mode 15-32  
inference  
confidence intervals 9-16  
hypothesis tests 9-9  
One-Proportion Z-Interval 9-18  
One-Sample Z-Interval 9-16  
One-Sample Z-Test 9-9  
Two-Proportion Z-Interval 9-19  
Two-Proportion Z-Test 9-12  
Two-Sample T-Interval 9-21  
Two-Sample Z-Interval 9-17  
infinite result R-19  
L
labeling  
axes 2-6  
parts of a sketch 14-5  
letters, typing 1-6  
library, managing aplets in 16-6  
linear fit 8-12  
infrared  
transmission of aplets between ma-  
chines 16-5  
initial guess 7-5  
input forms  
resetting default values 1-9  
Index  
I-5  
list  
low battery 1-1  
lowercase letters 1-6  
arithmetic with 13-7  
calculate sequence of elements 13-8  
calculating product of 13-9  
composed from differences 13-8  
concatenating 13-8  
counting elements in 13-9  
creating 13-1, 13-3, 13-4, 13-5  
deleting 13-6  
deleting list items 13-3  
displaying 13-4  
displaying list elements 13-4  
editing 13-3  
M
mantissa 10-16  
math functions  
complex number 10-8  
hyperbolic 10-10  
in menu map R-15  
keyboard 10-4  
logical operators 10-20  
menu 1-7  
polynominal 10-12  
probability 10-13  
real-number 10-15  
symbolic 10-19  
finding statistical values in list ele-  
ments 13-10  
generate a series 13-8  
generating series 13-8  
trigonometry 10-21  
math operations 1-18  
enclosing arguments 1-20  
in scientific notation 1-19  
negative numbers in 1-18  
matrices  
list function syntax 13-7  
list variables 13-1  
returning position of element in 13-9  
reversing order in 13-9  
sending and receiving 13-6  
sorting elements 13-9  
adding rows 15-23  
addition and subtraction 12-6  
arguments 12-10  
storing elements 13-1, 13-4, 13-5  
storing one element 13-7  
logarithm 10-4  
arithmetic operations in 12-6  
assembly from vectors 12-1  
changing row position 15-24  
column norm 12-10  
comma 13-7  
logarithmic  
fit 8-12  
functions 10-4  
logical operators  
AND 10-21  
commands 12-10  
equals (logical test) 10-20  
greater than 10-20  
greater than or equal to 10-20  
IFTE 10-21  
less than 10-20  
less than or equal to 10-20  
NOT 10-21  
condition number 12-10  
create identity 12-13  
creating 12-3  
creating in Home 12-5  
deleting 12-4  
deleting columns 15-23  
deleting rows 15-23  
determinant 12-10  
not equal to 10-20  
OR 10-21  
display eigenvalues 12-11  
displaying 12-5  
displaying matrix elements 12-5  
dividing by a square matrix 12-7  
dot product 12-10  
XOR 10-21  
logistic fit 8-12  
loop commands  
BREAK 15-23  
DO...UNTIL...END 15-22  
FOR I= 15-23  
editing 12-4  
extracting a portion 15-24  
finding the trace of a square matrix  
12-13  
inverting 12-7  
matrix calculations 12-1  
WHILE...REPEAT...END 15-22  
loop functions  
ITERATE 10-11  
RECURSE 10-11  
summation 10-11  
I-6  
Index  
multiplying and dividing by scalar  
12-6  
maximum real number 1-20, 10-9  
memory R-19  
multiplying by vector 12-7  
multiplying row by value and adding  
result to second row 15-24  
multiplying row number by value  
15-24  
clearing all R-5  
organizing 11-9  
out of R-20  
saving 1-24, 16-1  
viewing 11-1  
negating elements 12-7  
opening Matrix Editor 15-26  
redimension 15-24  
replacing portion of matrix or vector  
15-24  
sending or receiving 12-4  
singular value decomposition 12-12  
singular values 12-12  
size 12-12  
spectral norm 12-12  
spectral radius 12-12  
start Matrix Editor 15-23  
storing elements 12-3, 12-5  
storing matrix elements 12-5  
swap column 15-24  
swap row 15-24  
menu lists  
searching 1-8  
minimum real number 10-9  
Modes  
angle measure 1-9  
decimal mark 1-10  
number format 1-10  
multiple solutions  
plotting to find 7-8  
multiplication 10-4  
implied 1-19  
N
name conflict R-19  
naming  
transposing 12-13  
variables 12-1  
matrix functions 12-10  
COLNORM 12-10  
COND 12-10  
programs 15-4  
natural exponential 10-4, 10-10  
natural log plus 1 10-10  
natural logarithm 10-4  
negation 10-5  
negative numbers 1-18  
no equations checked R-19  
Normal Z-distribution, confidence inter-  
vals 9-16  
CROSS 12-10  
DET 12-10  
DOT 12-10  
EIGENVAL 12-11  
EIGENVV 12-11  
IDENMAT 12-11  
INVERSE 12-11  
note  
copying 14-8  
LQ 12-11  
LSQ 12-11  
editing 14-2  
importing 14-8  
LU 12-11  
MAKEMAT 12-11  
QR 12-12  
printing 15-25  
viewing 14-1  
writing 14-1  
RANK 12-12  
Notepad 14-1  
ROWNORM 12-12  
RREF 12-12  
SCHUR 12-12  
catalog keys 14-7  
creating notes 14-6  
writing in 14-6  
nrng 2-5  
SIZE 12-12  
SPECNORM 12-12  
SPECRAD 12-12  
SVD 12-12  
SVL 12-12  
TRACE 12-13  
nth root 10-6  
null hypothesis 9-3  
number format  
engineering 1-10  
fixed 1-10  
fraction 1-10  
TRN 12-13  
Index  
I-7  
in Solve aplet 7-5  
scientific 1-10  
Standard 1-10  
comparing 2-5  
connected points 8-16, 8-18  
decimal scaling 2-14  
defining the independent variable  
15-35  
numeric precision 11-9  
Numeric view  
adding X values 2-19  
automatic 2-17  
build your own table 2-19  
display defining function for column  
2-18  
recalculating 2-19  
setup 2-17, 2-19  
drawing axes 2-6  
expressions 3-3  
goto function 1-29  
grid points 2-6  
in Solve aplet 7-8  
index values 2-6  
integer scaling 2-14  
one-variable statistics 8-18  
overlay plot 2-14  
overlaying 2-16, 4-3  
scaling 2-14  
O
off  
automatic 1-1  
power 1-1  
On/Cancel 1-1  
scatter 8-15, 8-16  
sequence 2-6  
One-Proportion Z-Interval 9-18  
One-Sample T-Interval 9-20  
One-Sample T-Test 9-13  
One-Sample Z-Interval 9-16  
One-Sample Z-Test 9-9  
order of precedence 1-20  
overlaying plots 2-16, 4-3  
setting up 2-5, 3-2  
split-screen view 2-15  
splitting 2-15  
splitting into plot and close-up 2-14  
splitting into plot and table 2-14  
stairsteps 6-2  
statistical data 8-15  
statistics parameters 8-18  
t values 2-5  
P
π 10-9  
tickmarks 2-6  
paired columns 8-11  
Parametric aplet 4-1  
parametric variables  
Axes 15-30  
to capture current display 15-20  
tracing 2-8  
trigonometric scaling 2-14  
plotting resolution  
and tracing 2-8  
plot-view variables  
Area 15-30  
Connect 15-30  
Grid 15-31  
in menu map R-10  
Indep 15-32  
Labels 15-33  
Connect 15-30  
FastRes 15-31  
Function 15-30  
Grid 15-31  
Hmin/Hmax 15-31  
Hwidth 15-32  
Isect 15-32  
Labels 15-33  
Recenter 15-33  
RNG 15-34  
Root 15-33  
S1mark-S5mark 15-33  
StatPlot 15-34  
Tracing 15-32  
Ustep 15-34  
Recenter 15-33  
Ycross 15-36  
parentheses  
to close arguments 1-20  
to specify order of operation 1-20  
pause 15-28  
permutations 10-13  
pictures  
attaching in Sketch view 14-3  
plot  
analyzing statistical data in 8-20  
auto scale 2-14  
box-and-whisker 8-16  
cobweb 6-2  
I-8  
Index  
polar variables  
Axes 15-30  
running 15-7  
sending and receiving 15-8  
stopping 15-7  
structured 15-1  
Connect 15-30  
Grid 15-31  
in menu map R-11  
Indep 15-32  
prompt commands  
beep 15-25  
Labels 15-33  
Recenter 15-33  
Ycross 15-36  
create choose box 15-25  
create input form 15-27  
display item 15-26  
polynomial  
display message box 15-28  
halt program execution 15-28  
insert line breaks 15-28  
prevent screen display being updated  
15-27  
coefficients 10-12  
evaluation 10-12  
form 10-12  
roots 10-12  
set date and time 15-26  
store keycode 15-27  
Taylor 10-7  
polynomial functions  
POLYCOEF 10-12  
POLYEVAL 10-12  
POLYFORM 10-12  
POLYROOT 10-12  
position argument 15-20  
power (x raised to y) 10-6  
precedence 1-20  
predicted values  
statistical 8-21  
print  
Q
θ<εφαυλτ φοντ παρα>στεπ 2-5  
θrng 2-5  
quadratic  
extremum 3-6  
fit 8-12  
function 3-4  
quitting views 1-17  
quotes  
contents of display 15-25  
name and contents of variable 15-25  
object in history 15-25  
variables 15-25  
probability functions  
! 10-13  
in program names 15-4  
R
random numbers 10-14  
real number  
maximum 10-9  
minimum 10-9  
real part 10-8  
COMB 10-13  
permutations 10-13  
RANDOM 10-13  
UTPC 10-14  
UTPF 10-14  
UTPN 10-14  
real-number functions 10-15  
% 10-17  
%CHANGE 10-17  
%TOTAL 10-17  
CEILING 10-15  
DEGtoRAD 10-15  
FNROOT 10-15  
HMSto 10-16  
INT 10-16  
MANT 10-16  
MAX 10-16  
MIN 10-16  
UTPT 10-14  
program  
commands 15-5  
copying 15-8  
creating 15-4  
debugging 15-7  
deleting 15-8  
delimiters 15-1  
editing 15-5  
naming 15-4  
pausing 15-28  
printing 15-25  
MOD 10-17  
RADtoDEG 10-17  
ROUND 10-17  
SIGN 10-18  
Index  
I-9  
TRUNCATE 10-18  
XPON 10-18  
recalculation for table 2-19  
receive error R-20  
receiving  
S
S1mark-S5mark variables 15-33  
scaling  
automatic 2-14  
decimal 2-9, 2-10, 2-14  
integer 2-11, 2-14, 2-16  
options 2-14  
aplet 16-5  
lists 13-6  
matrices 12-4  
programs 15-8  
redrawing  
table of numbers 2-18  
reduced row echelon 12-12  
regression  
resetting 2-14  
trigonometric 2-14  
scatter plot 8-15, 8-16  
connected 8-16, 8-18  
SCHUR decomposition 12-12  
scientific number format 1-10, 1-19  
scrolling  
analysis 8-17  
fit models 8-12  
formula 8-12  
in Trace mode 2-8  
searching  
user-defined fit 8-12  
regulatory information  
Canada R-1  
USA R-1  
relative error  
menu lists 1-8  
speed searches 1-8  
secant 10-21  
sending  
aplets 16-5  
lists 13-6  
statistical 8-17  
resetting  
programs 15-8  
sequence  
aplet 16-4  
calculator R-4  
If calculator does not turn on R-5  
memory R-5  
definition 2-2  
sequence variables  
Axes 15-30  
Grid 15-31  
in menu map R-12  
Indep 15-32  
Labels 15-33  
Recenter 15-33  
Ycross 15-36  
result  
copying to edit line 1-21  
reusing 1-21  
root  
interactive 3-9  
nth 10-6  
variable 15-33  
root-finding  
setting  
date 15-26  
time 15-26  
displaying 7-7  
interactive 3-8  
operations 3-9  
variables 3-9  
sign reversal 7-6  
sine 10-4  
inverse hyperbolic 10-9  
singular value decomposition  
matrix 12-12  
running a program 15-7  
singular values  
matrix 12-12  
I-10  
Index  
sketches  
creating 14-5  
define one-variable sample 15-29  
define two-variable data set’s depen-  
dent column 15-29  
define two-variable data set’s inde-  
pendent column 15-29  
defining a fit 8-11  
creating a blank graphic 15-22  
creating a set of 14-5  
erasing a line 15-20  
labeling 14-5  
defining a regression model 8-11  
deleting data 8-10  
editing data 8-10  
frequency 15-29  
inserting data 8-11  
plot type 8-18  
plotting data 8-15  
predicted values 8-21  
regression curve (fit) models 8-11  
saving data 8-10  
opening view 14-3  
sets 14-5  
storing in graphics variable 14-5  
slope  
interactive 3-9  
soft key labels 1-2  
solve  
error messages 7-7  
initial guesses 7-5  
interpreting intermediate guesses  
7-7  
sorting data 8-11  
specifying angle setting 8-10  
toggling between one-variable and  
two-variable 8-11  
interpreting results 7-6  
plotting to find guesses 7-8  
setting number format 7-5  
solve variables  
tracing plots 8-20  
troubleshooting with plots 8-19  
zooming in plots 8-20  
statistics variables  
Axes 15-30  
Connect 15-30  
FastRes 15-31  
Grid 15-31  
in menu map R-13  
Indep 15-32  
Labels 15-33  
Recenter 15-33  
Ycross 15-36  
Axes 15-30  
Connect 15-30  
Grid 15-31  
Hmin/Hmax 15-31  
Hwidth 15-32  
in menu map R-14  
Indep 15-32  
Labels 15-33  
sorting 16-6  
aplets in alphabetic order 16-6  
aplets in chronological order 16-6  
elements in a list 13-9  
spectral norm 12-12  
spectral radius 12-12  
square root 10-5  
Recenter 15-33  
S1mark-S5mark 15-33  
Ycross 15-36  
step size of independent variable 15-35  
storing  
list elements 13-1, 13-4, 13-5, 13-7  
matrix elements 12-3, 12-5  
results of calculation 11-3  
value 11-2  
stack history  
printing 15-25  
stairsteps graph 6-2  
standard number format 1-10  
statistics  
strings  
literal in symbolic operations 10-20  
structured programming 15-1  
subtract 10-4  
summation function 10-11  
symbolic  
analysis 8-1  
analyzing plots 8-20  
angle mode 8-10  
calculate one-variable 15-29  
calculate two-variable 15-29  
computing 2VAR 8-11  
data set variables 15-39  
data structure 15-39  
calculations in Function aplet 10-22  
defining expressions 2-1  
differentiation 10-23  
Index  
I-11  
displaying definitions 3-8  
evaluating variables in view 2-3  
setup view for statistics 8-10  
symbolic functions  
| (where) 10-20  
ASEC 10-21  
COT 10-21  
CSC 10-21  
SEC 10-21  
sine, cosine, tangent 10-4  
trng 2-5  
equals 10-19  
ISOLATE 10-19  
troubleshooting R-1  
LINEAR? 10-19  
QUAD 10-19  
QUOTE 10-20  
truncating values to decimal places  
10-18  
tstep 2-5, 15-35  
Two-Proportion Z-Interval 9-19  
Two-Proportion Z-Test 9-12  
Two-Sample T-Interval 9-21  
Two-Sample T-test 9-14  
Two-Sample Z-Interval 9-17  
typing letters 1-6  
Symbolic view  
defining expressions 3-2  
syntax 10-3  
syntax errors 15-7  
T
table  
navigate around 3-7  
numeric values 3-7  
numeric view setup 2-17  
tangent 10-4  
inverse hyperbolic 10-9  
Taylor polynomial 10-7  
tickmarks for plotting 2-6  
time 10-16  
U
undefined  
name R-20  
result R-20  
un-zoom 2-11  
upper-tail chi-squared probability 10-14  
upper-tail normal probability 10-14  
upper-tail snedecor’s f 10-14  
upper-tail student’s t-probability 10-14  
user defined  
setting 15-26  
time, converting 10-16  
times sign 1-19  
tmax 15-35  
regression fit 8-12  
user prompts 15-25  
tmin 15-35  
too few arguments R-20  
tracing  
functions 2-8  
more than one curve 2-8  
not matching plot 2-8  
plots 2-8  
transmitting  
lists 13-6  
matrices 12-4  
programs 15-8  
transposing a matrix 12-13  
trigonometric  
functions 10-21  
scaling 2-11, 2-14, 2-16  
trigonometry  
cosine 10-9  
trigonometry functions  
ACOT 10-21  
ACSC 10-21  
I-12  
Index  
V
W
value  
warning symbol 1-7  
warranty R-2  
go directly to 3-7  
recall 11-3  
storing 11-2  
where command ( | ) 10-20  
variables  
X
xrng 2-5  
aplet 11-1  
categories 11-7  
definition 11-1, 11-7, R-7  
in equations 7-10  
in Symbolic view 2-3  
independent 15-35  
local 11-1  
Y
Ycross variable 15-36  
yrng 2-5  
previous result (Ans) 1-22  
printing 15-25  
Z
Z-Interval 9-16  
zoom 2-18  
root 15-33  
root-finding 3-9  
step size of independent 15-35  
types 11-1, 11-7  
use in calculations 11-4  
VARS menu 11-4, 11-5  
map R-8  
axes 2-12  
box 2-8  
center 2-8  
examples of 2-11  
factors 2-13  
in 2-9, 2-10  
vectors  
options 2-8, 3-7  
options within a table 2-18  
out 2-9, 2-10  
column 12-1  
cross product 12-10  
definition of R-7  
views 1-17  
redrawing table of numbers options  
2-18  
configuration 1-17  
definition of R-7  
square 2-9, 2-10  
un-zoom 2-11  
within Numeric view 2-18  
X-zoom 2-9, 2-10  
Y-zoom 2-9, 2-10  
Index  
I-13  

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