HP 39G, 40G User Manual

HP 39G/40G

GRAPHING CALCULATOR

USER’S GUIDE

Ver si on 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................................................................1 5-3 9

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 inf ormation

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 cal culator. 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 th em on to y o ur 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:

>6,1@, >&26@, >+20(@, etc.

• Shift keys, that is the key functions that you access by pressing the >6+,)7@ key first, are represented as follows:

>6+,)7@

CLEAR, >6+,)7@MODES, >6+,)7@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:

672?a,&$1&/a, 2.a

• 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*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 specifica lly disc laim s th e i mplie d warra nt ie s a nd 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.

and all rights are reserved. Reproduction, adaptation or translation of those prog rams without prior written p ermission of Hewlett Packard is prohibited.

P-2 Preface

Getting started

On/off, cancel operations

To turn on Press >21@ to turn on the calculator. To cancel When the calculator is on, the >21@ key cancels the current

operation.

To turn off Press >6+,)7@OFF to turn the calculator off.

To save power, the calculator turns itself off after several minutes of inactivity. All sto re d a nd d ispl ay ed information is saved.

If you see the ((•)) annunciator or the Low Bat message, then the calculator needs fresh ba tteries.

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 pro gram, or an editor), press >+20(@. All mathematical functions are available in the HOME. The name of the current aplet is displ ayed i n the title of the home view.

Getting started 1-1

The display

To adjust the contrast

To clear the display

Parts of the display

Simultaneously press >21@ and >@ (or >@) to increase (or decrease) the contrast.

• Press CANCEL to clear the edit line.

• Press >6+,)7@CLEAR to clear the edit line and the di splay history.

Title

History

Edit line

Menu key labels

Menu key or soft key labels. The labels for the menu keys’ current meanings. this picture. “Press

672?a

is the label for the first menu key in

672?a

” 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 (>+20(@) 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 c u rr e nt a pl et i s d is played at the top of the HOME view. RAD, GRD, DEG specify whether Radians, Grads or Degrees angle mode is set for HOME. The 'and ( symbolsindicate whether there is more history in the HOME display. Press the *e,and *k, to scroll in the HOME display.

NOTE

The HP 40G is packaged with a computerized algebra system

&$6_

(CAS). Press

to access the computerized algebra system. This User’s Guide contains images from the HP39G and do not display the

1-2 Getting started

&$6_

menu key label.

The keyboard

Menu keys

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 >6+,)7@ again.

α Alpha in effect for ne xt ke ys tr oke.

To cancel, press >$/3+$@ again.

((•)) Low battery power.

Busy.

Data is being transferred via infrared

or cable.

Menu key

labels

Menu keys

Aplet control

keys

Alpha key

Shift key

Getting started 1-3

Cursor

keys

Enter key

Aplet control keys

• On the calculator keyboard, the top row of keys are

called menu keys. Th eir 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 mea nings.

The aplet control keys are:

Key Meaning

>6<0%@ Displays the Symbolic view for the

current aplet. See “Symbolic view” on page 1-15.

>3/27@ Displays the Plot view for the current

aplet. See “Plot view” on page 1-15.

>180@ Displays the Numeric view for the

current aplet. See “Numeric view” on page 1-15.

>+20(@ Displays the HOME view. See

“HOME” on page 1-1.

>$3/(7@ Displays the Aplet Library menu. See

“Aplet library” on page 1-15.

>9,(:6@ 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

>21@ (CANCEL) Cancels the current operation if t he

calculator is on by pressing >21@. Pressing >6+,)7@, then calculator off.

>6+,)7@ Accesses the function printed in blue

above a key.

>+20(@ Returns to the HOME view, for

>$/3+$@ Accesses the alphabetical characters

>(17(5@ Enters an input or execu tes an

>@ Enters a negative number. To enter

>;75@ Enters the independent variable by

>'(/@ Deletes the character under the cursor.

CLEAR Clears all data on the screen. On a

>6+,)7@

*>,, *A,, *k,, *e,

CHARS Displays a menu of all available

>6+,)7@

performing calculations .

printed in orange below a key. Hold down to enter a string of characters.

operation. In calculations, >(17(5@ acts

like “=”. When as a menu key, >(17(5@ acts the same as pressing

–25, press >@25. Note: this is not the

same operation tha t the su btract button performs (

inserting X, T, θ, or N into the e dit line, depending on the current active aplet.

Acts as a backspace key if the cursor is at the end of the line.

settings screen, for example Plot Setup, >6+,)7@ to their default values.

Moves the cursor around the display. Press beginning, end , top or bottom.

characters. To type one, use the arrow keys to highlight it, and press select multiple characters, select each and press

OFF turns the

2.a

67$57a

is present

2.a

67$57a

>@).

CLEAR returns all settings

>6+,)7@ first to move to the

2.a

(&+2a

, then press

2.a

. 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:>6+,)7@ and >$/3+$@.

Key Description

>6+,)7@ Press the >6+,)7@ key to access the

operations printed in blue above the keys. For instance, to access the Modes screen, press >6+,)7@, then press >+20(@.

MODES is labelled in blue above the

( >+20(@ key). You do not need to hold down >6+,)7@ when you press HOME. This action is d epicte d in this m anua l as

“press >6+,)7@

MODES.”

To cancel a shift, press >6+,)7@ again.

>$/3+$@ The alphabetic keys are also shi fted

keystrokes. For instance, to type Z, press >$/3+$@Z. (The letters are printed in orange to the lower right of each key. )

To cancel Alpha, press >$/3+$@ again. For a lower case letter, press

>6+,)7@>$/3+$@. For a string of letters, hold down

>$/3+$@ while typing.

HELPWITH The HP 39G built-in help is available in HOME only. It

provides syntax help for built-in math fun ction s . Access the HELPWITH command by pressing >6+,)7@

and then the math key for which yo u require syntax help.

Example Press>6+,)7@

SYNTAX

>[@ >(17(5@

Note: Remove the left parenthesis from built-in commands such as sine, cosine, and tangent before invoking the HELPWITH command.

1-6 Getting started

SYNTAX

Math keys HOME (>+20(@) is the place to do calculations.

Keyboard keys. The most common operations are available from the keyboard, such as the arithmetic (like >@) and trigonometric (like >6,1@) functions. Press >(17(5@ to complete the operation: >6+,)7@√ 256>(17(5@ displays 16.

MATH menu. Press >0$7+@ to open the MATH menu. The MATH menu is a comprehensive list of math functions that do not appear on the keyboard. It also incl udes categories for all other functions and constants. The functions are grouped by category, ranging in alphabetical order from Calculus to Trigon ometry.

– 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,).

2.a

to insert the selected com mand on to the ed it

&$1&/a

to dismiss the MATH menu without

&216a

displays the list of Program

07+a

takes you to the beginning of the

HINT

– Press

line.

– Press

selecting a command.

– Pressing

Constants. You can use these in programs that you develop.

– Pressing

MATH menu.

See “Math functions by category” on page 10-3 for details of the math functions.

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 beginnin g with that alpha chara cte r. With this method, you do not ne e d to press >$/3+$@ first. Just press the key that corresponds to the comma nd’s beginning alpha character.

Program commands

Pressing >6+,)7@CMDS d isplays 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

To search a menu • Press *e, or *k, to scroll through the list. If you press

• If there are two columns, the left column shows general

• To speed-search a list (with no edit line), type the first

arrow in the display

means more items below.

A_

arrow in the display

means more items above.

>6+,)7@*e, or >6+,)7@*k,, you’ll go all the way to the end or the beginning of the list. Highlight the item you want

2.a

to select, then press

(or >(17(5@).

categories and the right colu mn 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

2.a

or >(17(5@when you have

highlighted your selection.

letter of the word. For example, to find the Matrix category in >0$7+@, press >@, the Alpha“M”key.

• To go up a page, you can press >6+,)7@*>,. To go down a

page, press >6+,)7@*A,.

To cancel a menu Press >21@ (for CANCEL) or

&$1&/a

. This cancels the current

operation.

1-8 Getting started

Input forms

An input form shows several fields of information for you to examine and specify. After highlighting the fie ld to edit, you can enter or edit a number (or expression). You can also select

&+226a

options from a list ( to check (

_&+.a

). See below for an example of an input form.

). Some input forms include items

Reset input form values

To reset a default field va lue in an input f orm, move the cursor to that fi eld and pr ess >'(/@. To re set all default field value s in the input form, press >6+,)7@

Mode settings

You use the Modes input form to set the modes for HOME.

HINT

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 con f igure an aplet, you use the SETUP keys (>6+,)7@>3/27@ and >6+,)7@>180@).

Press >6+,)7@MODES to access the HOME MODES input form.

Setting Options

Angle Measure

Angle values are:

Degrees. 360 degrees in a circle. Radians. 2π radians in a circle. Grads. 400 grads in a circle.

The angle mode you set is the angle setting us ed in both HOME a n d the current aplet. This is done to ensure that trigonometric calculations done in the current aplet and HOME gi ve the same result.

CLEAR.

Getting started 1-9

Setting Options (Continued)

Number Format

Decimal Mark

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 specifi ed number of decimal places. Example: 123.456789 becomes 1.23E2 in Scientific 2 fo rmat.

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 fraction s” on page 1-24. 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 list s and mat rices, and to separate function arguments. Comma mode uses periods (dot) as separators in these contexts.

1-10 Getting started

Setting a mode

HINT

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 >6+,)7@MODES to open the HOME MODES input form.

The cursor (highlight) is in the first field, Angle Measure.

&+226a

2. Press

to display a

list of choices.

3. Press*k,to select Degrees,



and press

2.a

. The angle mea s ur e changes to degrees.

4. Press>+20(@ to return to HOME.

Whenever an input form has a list of choices for a field, you can press >@ to cycle through them instead of using

&+226a

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 va ri e ty of so urces:

• 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 configuratio n ” on page 1-17 for further information.

Aplet

Use this aplet to explore:

name

Function Real-valued, rectangular functions y in

terms of x. Example: .

y 2x23x 5++=

Inference Confidence intervals and Hypothesis tests

based on the Normal and Students-t distributions.

Parametric Parametric relations x and y in terms of t.

Example: x = cos(t) an d y = sin(t).

Polar Polar functions r in terms of an angle θ.

Example: .

r 24θ()cos=

Sequence Sequence functions U in terms of n, or in

terms of previous terms in the same or another sequence, such as and

. Example: , and

n 2–

U10= U21=

n 1–

Solve Equations in one or more real-valued

variables. Example: .

x 1+ x

n 1–

x–2–=

Statistics One-var iable (x) or two-var iable (x and y)

statistical data.

In addition to these aplets, which can be used in a variety of applications, the HP 39G/40 G 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 educa tors, 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 Qu ad Explo rer aplet is used to inve stigate the behaviour of as the values of a, h and v change, bo th

yaxh+()

v+= by manipulating the equation and seeing the change in the graph, and by manipulating the graph and seeing the change in the equation.

HINT

More detailed documentation, and an accompanying student

work sheet can be found at HP’s web site.

When first started, the aplet is

*53+aa

mode, in which the arrow keys, the >@ and >@ keys and the>@ key are used to change the shape of the graph. This changing shape is reflected in t he equation displayed at the top right corner of the screen, while the original graph is retained for comparison. In this mode th e graph controls the equation.

It is also possibl e to have the equation control the gra ph. Pressing

6<0%a

displays a

sub-expression of your equation (see right).

Pressing the *A,and *>,key moves between subexpressions, while pressing the *k,and*e, key changes their values.

/(9(/a

Pressing

allows the user to select wheth er all three sub-

expressions will be explored at once or only one at a time. A

7(67a

button is provided to

evaluate the student’s knowledge. Pressing

7(67a

displays a target quadratic graph. The student must manipulate the equation’s parameters to make the equation match the target graph. Wh en a student feels that they have

&+(&.a

correctly chosen the parameters a answer and provide feedback. An

button evaluates t he

$16:a

button is provided

for those who give up!

Getting started 1-13

Trig Explorer aplet

The Trig Explorer aplet is used to investigate the behaviour of the graph of as the values of a, b, c

ya bxc+()d+sin=

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 equa tion.

67$57a

When the user presses

$3/(7a

in the

view, the screen

shown right is displ a yed.

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.

25,*aa

and

is a

Origin

The button labelled toggle between

(;75aa

. When

25,*aa

chosen, the ‘point of control’ is at the origin (0,0) and the *k,*e, and *>,*A, keys control vertical and horizontal

(;75aa

transformations. When is chosen the ‘point of control’ is on the first extremum of the graph (i.e. for the sine gr aph at .

π 21,⁄()

The arrow keys change the amplitude and frequency of the

Extremum

graph. This is most easily seen by experimenting.

Pressing >6<0%@ displays the equation at the top of the screen. The equation is controls the graph. Pressing the *A, and *>, keys move s from parameter to parameter. Pressing the *k, or *e, key changes the parameter’s va lue s .

The default angle setting for this aplet is radians. The angle

5$'aa

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 >$3/(7@ to display the Aplet library menu. Select the

aplet and press From within an aplet, you can return to HOME any time by

pressing >+20(@.

67$57_

or >(17(5@.

Aplet views

When you have configured an aplet to define the relation or data that you want t o explore, you can display i t in different views. Here are illustrations of the three major apl et vi ews (Symbolic, Plot, an d Numeric), th e six supporting aplet views (from the VIEWS menu), and the two user-defined views (Note and Sketch).

Symbolic view Press >6<0%@ to display the aplet’s Symbolic view.

Y o u use this view to define the function(s) or equation(s) that you want to explor e.

See “About the Symbolic view” on page 2-1 for further information.

Plot view Press >3/27@ 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 >180@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. >9,(:6@

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.

2.a

Plot-Detail view

Overlay Plot view

The VIEWS menu contains the Plo t-Detail view. >9,(:6@

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.

The VIEWS menu contains the Overlay Plot view.

>9,(:6@

Select Overlay Plot Plots the current expression(s)

without erasing an y pre existing plot(s) .

See “Other views for scaling and splitting the graph” on page 2-13 for further information.

2.a

Note view Press >6+,)7@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 furthe r information.

Sketch view Press >6+,)7@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 (>6+,)7@>3/27@,and >6+,)7@>180@) to configure the aplet. For example, pr ess >6+,)7@ (>6+,)7@>3/27@)to display the input form for setting the aple t’s plot settings. Angle measure is controlled using the view.

Plot Setup Press>6+,)7@SETUP-PLOT. Sets

parameters to plot a graph.

Numeric Setup Press >6+,)7@SETUP-NUM. Sets

parameters for building a table of numeric valu es .

SETUP-PLOT

MODES

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 (>6+,)7@

SYMB.

SETUP

To change views Each view is a separate environment. To change a view, select

a different view by pressing >6<0%@, >180@, >3/27@ keys or select a view from the VIEWS menu. To change to HOME, press >+20(@. You do not explicitly close the current view, you just enter anot her one—like passing from one room into another in a house. Data that you enter is automati cally sav ed as you enter it.

To save aplet configuration

Getting started 1-17

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.

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 (>0$7+@).

To access programming command s, press >6+,)7@

“Programming commands” on page 15-14 for further information.

CMDS. See

Where to start The home base for the calculator is the HOME view

(>+20(@). You can do all calculations here, and you can access all >0$7+@ operations.

Entering expressions

Example Calculate :

• Enter an expression into the HP 39G/40G in the same left-to-right order that you would write th e 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 o ut its name.

• Press >(17(5@ to evaluate the expression you have in the edit line (where the blinking cursor is). An expression can contain numbers, functi ons, and variables.

14 8–

----------------------------

>@23>[, >@14 >;@>6+,)7@√ 8>@ >j@>@3 >OQ@45 >@ >(17(5@

3–

45()ln

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

6+2:a

it and then press

Negative numbers

1-18 Getting started

Type >@to start a negative numb er or to insert a nega tiv e sign.

To raise a negative number to a power, enclose it in parentheses. For example, (–5)

= 25, whereas –52 = –25.

Scientific notation (powers of 10)

A number like or is written in scientific notation, that is, in terms of powers of ten. This is simpler to

work with than 5000 0 or 0.0000 00321. To e nter numbe rs like these, use

Example Calculate

>@4 >6+,)7@EEX >@13>@ >;@>@6 >6+,)7@

23>@ >j@ 3 >6+,)7@EEX >@5

>(17(5@

510

× 3.21 107–×

EEX. (This is easier than using >;@10>[N@.)

13–

410

×()610

---------------------------------------------------310

EEX

×()

5–

Explicit and implicit multiplication

HINT

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 AB as A*B.

Implied multiplication will not alway s work as expect ed. For example, entering A(B+4) will not give A*(B+4). Instead

an error message is displ ayed: “Invalid User Function”. T his is because the calculator interprets A(B+4) as meaning ‘evaluate function A at the va l u e B+4’, and function A does 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...

>6,1@ 45>@ >6+,)7@π sin (45 + π) >6,1@45>@ >@>6+,)7@π sin (45) + π

Algebraic precedence order of evaluation

Largest and smallest numbers

>6+,)7@√85>;@ 9 >6+,)7@√>@ 85>;@9>@

Functions within an expression are evalu ated 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.

2. Prefix functions, such as SIN and LOG.

3. Postfix functions, such as !

4. Power function, ^, NTHROOT.

5. Negation, multi plication, and division.

6. Addition and subtraction.

7. AND and NOT.

8. OR and XOR.

9. Left argument of | (where).

10. E quals, =.

The smallest number the HP 39G/40G can represent is

–499

1×10 largest number is 9.99999999999 × 10

still displayed as this number.

(1E–499). A sma ller result is displa yed as zero. The

85 9× 85 9×

–49

. A larger result is

1-20 Getting started

+ 258 hidden pages