HP 39gs Graphing Calculator, 40gs Graphing Calculator User Manual

hp 39gs and hp 40gs graphing calculators

Mastering the hp 39gs & hp 40gs

A guide for teachers, students and other users of the hp 39gs & hp 40gs

Edition 1.0

HP part number F2224-90010

Notice

THIS MANUAL AND ANY EXAMPLES CONTAINED HEREIN ARE PROVIDED "AS IS" AND ARE SUBJECT TO CHANGE WITHOUT NOTICE. HEWLETT-PACKARD COMPANY MAKES NO WARRANTY OF ANY KIND WITH REGARD TO THIS MANUAL, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY, NON-INFRINGEMENT AND FITNESS FOR A PARTICULAR PURPOSE.

HEWLETT-PACKARD CO. SHALL NOT BE LIABLE FOR ANY ERRORS OR FOR INCIDENTAL OR CONSEQUENTIAL DAMAGES IN CONNECTION WITH THE FURNISHING, PERFORMANCE, OR USE OF THIS MANUAL OR THE EXAMPLES CONTAINED HEREIN.

Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws.

Hewlett-Packard Company

16399 West Bernardo Drive, MS 8-600

San Diego, CA 92123

USA

Acknowledgements

Hewlett-Packard would like to thank the author Colin Croft.

Printing History Edition 1 December 2006

Table of Contents

Introduction .......................................................................................................................7

Getting Started ..................................................................................................................9

Some Keyboard Examples ...............................................................................................10

Keys & Notation Conventions ..........................................................................................11

Everything revolves around Aplets! .................................................................................14

The HOME view ...............................................................................................................18

What is the HOME view? .............................................................................................18

Exploring the keyboard ...............................................................................................19

Angle and Numeric settings .........................................................................................28

Memory Management .................................................................................................30

Fractions on the hp 39gs and hp 40gs .........................................................................33

The HOME History .......................................................................................................37

Storing and Retrieving Memories .................................................................................39

Referring to other aplets from the HOME view.............................................................40

A brief introduction to the MATH Menu ........................................................................41

Resetting the calculator................................................................................................42

Summary ....................................................................................................................45

The Function Aplet ...........................................................................................................46

Auto Scale ...................................................................................................................49

The PLOT SETUP view...................................................................................................50

The default axis settings ..............................................................................................52

The Bar ............................................................................................................52

The Menu Bar functions ...............................................................................................53

The FCN menu .............................................................................................................57

The Expert: Working with Functions Effectively ................................................................62

The VIEWS menu..............................................................................................................85

Downloaded Aplets from the Internet ..........................................................................91

The Parametric Aplet .......................................................................................................92

The Expert: Vector Functions ............................................................................................95

Fun and games............................................................................................................95

Vectors ........................................................................................................................96

The Polar Aplet................................................................................................................98

The Sequence Aplet..........................................................................................................99

The Expert: Sequences & Series......................................................................................102

The Solve Aplet..............................................................................................................105

The Expert: Examples for Solve......................................................................................113

The Statistics Aplet - Univariate Data..............................................................................114

The Expert: Simulations & random numbers...................................................................120

The Statistics Aplet - Bivariate Data................................................................................123

The Expert: Manipulating columns & eqns......................................................................133

The Inference Aplet ........................................................................................................141

The Expert: Chi2 tests & Frequency tables .......................................................................147

The Linear Solver Aplet ..................................................................................................150

Example 1 .................................................................................................................150

Example 2 .................................................................................................................150

Example 3 .................................................................................................................151

The Triangle Solve Aplet ................................................................................................152

Example 1 .................................................................................................................152

Example 2 .................................................................................................................153

Example 3 .................................................................................................................154

The Finance Aplet ..........................................................................................................155

The Quad Explorer Teaching Aplet .................................................................................159

The Trig Explorer Teaching Aplet....................................................................................162

The MATH menus...........................................................................................................165

Accessing the MATH menu commands........................................................................166

The PHYS menu commands........................................................................................168

The MATH menu commands.......................................................................................169

The ‘Real’ group of functions .....................................................................................170

The ‘Stat-Two’ group of functions ..............................................................................178

The ‘Symbolic’ group of functions ..............................................................................179

The ‘Tests’ group of functions ....................................................................................182

The ‘Trigonometric’ & ‘Hyperbolic’ groups of functions ..............................................182

The ‘Calculus’ group of functions ...............................................................................184

The ‘Complex’ group of functions ..............................................................................186

The ‘Constant’ group of functions ..............................................................................189

The ‘Convert’ group of functions ...............................................................................189

The ‘List’ group of functions .......................................................................................190

The ‘Loop’ group of functions ....................................................................................193

The ‘Matrix’ group of functions..................................................................................195

The ‘Polynomial’ group of functions...........................................................................202

The ‘Probability’ group of functions ...........................................................................205

Working with Matrices ..................................................................................................209

Working with Lists.........................................................................................................215

Working with Notes & the Notepad...............................................................................217

Independent Notes and the Notepad Catalog ............................................................219

Creating a Note .........................................................................................................220

Working with Sketches..................................................................................................222

The DRAW menu........................................................................................................223

Copying & Creating aplets on the calculator...................................................................226

Different models use different methods to communicate.............................................227

Sending/Receiving via the infra-red link or cable.......................................................228

Creating a copy of a Standard aplet. .........................................................................230

Some examples of saved aplets ................................................................................232

Storing aplets & notes to the PC.....................................................................................237

Overview ..................................................................................................................237

Software is required to link to a PC ...........................................................................238

Sending from calculator to PC ....................................................................................239

Receiving from PC to calculator..................................................................................244

Aplets from the Internet.................................................................................................245

Using downloaded aplets ..........................................................................................249

Deleting downloaded aplets from the calculator ........................................................250

Capturing screens using the Connectivity Kit ..............................................................251

Editing Notes using the Connectivity Software................................................................252

Programming the hp 39gs & hp 40gs ............................................................................255

The design process ....................................................................................................255

Planning the VIEWS menu .........................................................................................257

The SETVIEWS command ............................................................................................259

Example aplet #1 – Displaying info............................................................................262

Example aplet #2 – The Transformer Aplet.................................................................268

Designing aplets on a PC ...........................................................................................270

Example aplet #3 – Transformer revisited ..................................................................272

Example aplet #4 – The Linear Explorer aplet ............................................................274

Alternatives to HP Basic Programming...........................................................................281

Flash ROM.....................................................................................................................284

Programming Commands ..............................................................................................286

The Aplet commands .................................................................................................286

The Branch commands...............................................................................................287

The Drawing commands ............................................................................................289

The Graphics commands ............................................................................................291

The Loop commands ..................................................................................................291

The Matrix commands ...............................................................................................292

The Print commands ..................................................................................................293

The Prompt commands ..............................................................................................294

Appendix A: Some Worked Examples............................................................................298

Finding the intercepts of a quadratic ..........................................................................298

Finding complex solutions to a complex equation ......................................................299

Finding critical points and graphing a polynomial......................................................300

Solving simultaneous equations.................................................................................302

Expanding polynomials .............................................................................................304

Exponential growth ...................................................................................................305

Solution of matrix equations......................................................................................307

Finding complex roots ...............................................................................................308

Complex Roots on the hp 40gs ..................................................................................309

Analyzing vector motion and collisions ......................................................................310

Circular Motion and the Dot Product ..........................................................................311

Inference testing using the Chi2 test............................................................................312

Appendix B: Teaching or Learning Calculus....................................................................314

Investigating the graphs of y=xn for n an integer ....................................................314

Domains and Composite Functions .............................................................................315

Gradient at a Point ....................................................................................................317

Gradient Function ......................................................................................................318

The Chain Rule...........................................................................................................319

Optimization .............................................................................................................319

Area Under Curves ....................................................................................................320

Fields of Slopes and Curve Families ...........................................................................320

Inequalities................................................................................................................321

Rectilinear Motion......................................................................................................321

Limits.........................................................................................................................321

Piecewise Defined Functions ......................................................................................322

Sequences and Series ................................................................................................322

Transformations of Graphs ........................................................................................323

Appendix C: The CAS on the hp 40gs .............................................................................324

Introduction ...............................................................................................................324

Using the CAS ............................................................................................................327

Examples using the CAS ............................................................................................341

The CAS menus ..........................................................................................................358

On-line help ..............................................................................................................361

Configuring the CAS...................................................................................................362

Tips & Tricks - CAS .....................................................................................................366

NNTTRROODDUUCCTTIIOON

This book is intended to help you to master your hp 39gs or hp 40gs calculator but will also be useful to users of earlier models such as the hp 39g, hp 40g and hp 39g+. These are very sophisticated calculators, having more capabilities than a mainframe computer of the 1970s, so you should not expect to become an expert in one or two sessions. However, if you persevere you will gain efficiency and confidence.

The hp 39gs vs. the hp 40gs

The hp 39gs and hp 40gs, shown above, are ‘sister’ calculators released in 2006. They are identical in almost all respects except for their color schemes and in whether they have infra-red or a CAS. The hp 39gs was released mainly in the United States and other regions, such as Australia, which do not allow a Computer Algebra System, or CAS, in their educational systems. The hp 40gs, on the other hand, was released mainly in Europe where a CAS has long been an expected ability for calculators used by high school students. The hp 39gs has infra-red communication, similar to that of a TV remote control, which allows easy transmission of programs and aplets between calculators. The hp 40gs does not and uses a cable instead.

Many of the markets targeted by the hp 40gs do not allow infra-red communication in assessments and so, on the hp 40gs, this ability is permanently disabled, substituting instead a mini-serial cable supplied with the calculator (see page 237). The previous models, the hp 39g & hp 40g shared a common chip and, although it was never intended to be possible, a hacker released a special aplet for the hp 39g which would ‘convert’ it into an hp 40g and activate the CAS. This is not the case with the hp 39gs & hp 40gs: the internal chips are different and there is no way to ‘convert’ one into the other using an aplet or program.

For more information on the CAS, see page 324. This manual will cover, for the most part, the features which are shared by both calculators with the CAS covered in Appendix C. A detailed manual for the CAS is also supplied with the hp 40gs and more information can be found on the official HP website and on the author’s website The HP HOME view at

http://www.hphomeview.com

The majority of readers of this manual may only have used a Scientific calculator before so explanations are as complete as possible. However it is not the purpose of this book to teach mathematics and knowledge will largely be assumed. Those already familiar with another brand or type of calculator may find a quick skim sufficient, concentrating perhaps on the ‘Expert User’ chapters.

This book provides a supplement to the official manual and, more importantly, expert tips to make your work smother and more confident. It has been designed to cover the full use of the hp 39gs and hp 40gs calculators. This means explanations which will be useful to anyone from a student who is just beginning to use algebra seriously, to one who is coming to grips with advanced calculus, and also to a teacher who is already familiar with some other brand of graphic calculator.

The impact graphical calculators are having on the topics taught and even more, the way they are taught is proving to be profound. The inventiveness and flexibility of teachers of mathematics is being stretched to the limit as we gradually change the face of teaching in the light of these machines. For those concerned with the impact of a graphical calculator on the ‘fundamentals’ of mathematics, it should be recalled that the same fears were held for scientific calculators when they were introduced to schools. History has shown that these fears were generally groundless. Students are learning topics in high school that their parents did not cover until university years. In particular, the scientific calculator proved to be a great boon to students of middle to lower ability in mathematics, relieving them of the burden of tedious calculations and allowing them to concentrate on the concepts. It is my opinion, as a practicing mathematics teacher of some 25 years, that this is also the case with graphical calculators.

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Let’s begin by looking at the fundamentals - the layout of the keyboard and the positions of the important keys used frequently. The sketch below shows most of the important keys. As can be seen on the previous pages, the keyboards for the hp 39gs and hp 40gs are exactly the same except for the different color schemes. These keys are the ones which control the operation of the calculator – most others are simply used to do calculations once the important keys have set up the environment to do it in.

The NUM key gives you a tabular view of your function, sequence or data.

The PLOT key displays the graph view for any given environment.

The SYMB key nearly always takes you to a view in which you can enter e

uations.

TTAARRTTEED

These six screen keys change their function in different contexts. The bar at the bottom of the screen labels them. Check this bar for special functions in any given context.

These are the arrow keys. They let you move within a screen.

The VIEWS key gives a different menu in each aplet. It can be very useful, and is always worth checking.

HOME is where you will do most of your calculations. It is shared by all the aplets and oversees them all.

The ALPHA key accesses the alphabetical chars below most buttons.

The SHIFT key accesses the extra functions above most buttons.

The APLET key is central. This key allows you to choose which mathematical environment you wish to work in.

Examples of the effects of each of these keys and many more are shown on the pages that follow.

OOMME

Shown below are snapshots of some typical screens (called “views”) which you might see when you press the keys shown on the previous page. Exactly what you see depends on which aplet is active at the time. See page

The Function aplet is used below to illustrate this. The normal use of the Function aplet is to graph and analyze Cartesian functions. Notice at the bottom of the various screens how the meanings of the row of unlabelled screen keys change in different views.

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14 for an introduction to aplets.

SYMB key - in this case it is set to graph

The

the function

XXAAMMPPLLEES

= x − x2 − 7 x + 6 .x

()

PLOT key - used to graph the function.

The

PLOT SETUP view sets the axes.)

(The

The NUM key showing a tabular view of the function.

NUM SETUP view sets table parameters.)

(The

The

APLET key is used to choose which aplet is active. There are 12

aplets provided with the calculator and more can be downloaded from the internet.

The MATH key gives access to more than a hundred extra functions, grouped into categories. The view shown right is part of the Probability section.

There are a number of types of keys/buttons that are used on the hp 39gs and hp 40gs.

The basic keys are those that you see on any calculator including scientific ones, such as the numeric operators and the trig keys. Most of these keys have two or more functions, with the second function accessed via the

In this book, all references to buttons, whether they need the

KEY.

The SHIFT and ALPHA keys

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SHIFT key and the alphabetic character accessed via the ALPHA key.

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OONNVVEENNTTIIOONNS

Take for example the you get the right you will see two additional meanings assigned via the

ALPHA keys.

and

COS function. However above left of the key and below

COS key shown left. If you just press the key,

SHIFT key or not, are written in this typeface:

SHIFT

SHIFT key gives you the second function for each key. In the case of the

The

COS key, the second function is ACOS, sometimes referred to as arc-cos or cos

or inverse cos. Most keys have these second functions that are obtained via the

SHIFT key.

Note: When I want you to use one of these keys that needs to have the key pressed first I usually won’t say so. It seems to me that you’re intelligent enough to work out for yourself when the

The ALPHA key

The next modifier key is the characters, and these appear below and right of most keys. Pressing before the the calculator can be locked in can also simply hold down the

ALPHA key will give lower case alphabetic characters. In many views

ALPHA key. This is used to type alphabetic

ALPHA mode using one of the screen keys. You

ALPHA key.

SHIFT key needs to be pressed.

SHIFT

-1

The Screen keys

A special type of key unique to the hp 39gs, hp 40gs and family is the row of blank keys directly under the screen. These keys change their function depending on what you are doing at the time. The easiest way to see this is to press the

APLET key. As you can see right, the functions

are listed at the bottom of the screen. All you have to is to press the key under the screen definition you want to use. These buttons are normally referred to as SK1 to SK6, where SK is “Screen Key”.

All references to keys of this type are shown as images of the label. For example, if I want you to press the key under the SORT label it would be written as

. Do it now and you’ll see the screen shown on the right. Notice that the keys have now changed function. Press the one under

to return to the previous view.

Pop-up menus & short-cuts

Sometimes pressing a key pops up a menu on the screen as you just saw. You use the up/down arrow keys to move the highlight through the menu and make choices by pressing the listed in a menu will usually be written using italics. As an example, I might say to press

ENTER key. Choices that are

and choose

Chronologically. The manual you are given with your calculator uses a different convention.

As mentioned before, the third way a key can be used is to get letters of the alphabet. This is not so that you can write letters to your friends (although you can do that with the Notepad) but so that you can use variables like X and Y or A and B. The key above the alphabet. Lower case letters are obtained by pressing the type in more than just a single letter, hold down the

SHIFT key labeled ALPHA is used to type in letters of the

SHIFT key before the ALPHA key. If you want to

ALPHA key. Unfortunately, this doesn't work for

lowercase.

Try this…

If you haven’t already, Press the

HOME key to see the screen on the right. Yours may not be

out of the menu from the previous screen.

blank like mine but that doesn’t matter.

1 2 and then press the screen key labeled , circled on the

Press image. Now press the

XTθ key). Finally, press the ENTER key. Your screen should look

the like the one on the right. You have now stored the value

D. Each alpha key can be used as a memory.

Note that memories

ALPHA key and then the alphabetic D key (on

12 into memory

X, T and θ are regularly overwritten by the normal

operation of the calculator and should be used with caution.

You can also use these memories in calculations. Type in the following, not forgetting the

ALPHA key before the D….

(3+D)/5 ENTER

The calculator will use the value of haven’t worked it out for yourself, the multiply key

12 stored earlier in D to evaluate the expression (see image). In case you

/ symbol comes from the divide key and the * symbol from the

More information on memories and detailed information on the HOME view in general is given on pages 39.

The calculator also comes with an immense number of mathematical functions. They can all be obtained via menus through the from the keyboard. Try pressing the

MATH key now and you should

MATH key or

find your screen looks like the screen shot left.

MATH menu is covered in detail on pages 165 but we will have a brief look now.

The

The left side of the menu lists the categories of functions. As you use the up/down arrows to scroll through the topics, you’ll see the actual list on the right change. Move down through the menu until you reach Prob. (short for Probability) and then one step more and you’ll find yourself back at Real. Now press the right arrow key and your highlight will move into the right hand menu (see above). Move the highlight down through this menu until you reach Round. Press

ENTER.

You should now be back the display as shown right. You can also achieve the same effect by

ALPHA to type in the word letter by letter. Many people prefer to

using do it that way.

Now type in:

4+D/18,3) and press ENTER

As you can see, the effect was to round off the answer of 4 3 decimal places. Entering

ROUND(4+D/18,-3) would have rounded to

3 significant figures instead.

There are shortcuts for obtaining things from the

MATH menu that are

covered later (see page 41).

HOME, with the function ROUND( entered in

666666.. to

VVEERRYYTTHHIINNGGRREEVVOOLLVVEESSAARROOUUNND

A built in set of aplets are provided in the and hp 40gs. This effectively mean that it is not just one calculator but a dozen (or more), changing capabilities according to which aplet is chosen.

The best way to think of these aplets is as “environments” or “rooms” within which you can work. Although these environments may seem dissimilar at first, they all have things in common, such as that the produces graphs, that the

NUM key displays the information in tabular form.

There are twelve standard aplets available via the the Internet (see pages 255 & 245). These aplets are:

SYMB key puts you into a screen used to enter equations and rules, and that the

APLET view on the hp 39gs

APLET key. More can be created by you or obtained via

PPLLEETTS

PLOT key

The Finance aplet (see page 155)

Performs calculations involving time/value of money.

The Function aplet (see page 46)

Provides f(x) style graphs, calculus functions etc. It will not only graph but find intercepts, intersections, areas and turning points.

The Inference aplet (see page 141)

Allows the investigation of inferential statistics via hypothesis testing and confidence intervals.

The Linear Solver aplet (see page 150 )

This aplet is used to solve simultaneous linear equations in two or three unknowns.

The Parametric aplet (see page 92)

Handles x(t), y(t) style graphs. Can also be used to help with vector motion.

The Polar aplet (see page 98)

Handles r(θ) style graphs. Quite apart from their mathematical use, they produce some really lovely patterns!

The Quadratic Explorer aplet (see page 159)

This is a teaching aplet, allowing the student to investigate the properties of quadratic graphs using an interactive format which allows the connection between the coefficients and the graph to be easily seen.

The Sequence aplet (see page 99)

(

Handles sequences such as T

recursive and non-recursive sequences.

+ 3; T1 = 2 or T = 2

n−1

The Solve aplet (see page 105)

n−1

. Allows you to explore

Solves equations for you. Given an equation such as A

variable if you tell it the values of the others.

2πr r + h

it will solve for any

)

The Statistics aplet (see page 114 & 123)

Handles descriptive statistics. Data entry is easy, as is editing. It analyzes univariate and bivariate data, drawing scatter graphs, histograms and box & whisker graphs and finding lines of best fit, linear and non-linear.

The Triangle Solve aplet (see page 152 )

This aplet solves for sides and angles in triangles.

The Trig Explorer aplet (see page 162)

This is a teaching aplet, allowing the student to investigate the properties of sine and cosine graphs in the same interactive fashion as the Quadratic Explorer.

The Function aplet is probably the easiest to understand and also the one you will use most often, so we will have a very quick look at the commonly seen views of this aplet.

Some typical aplet views

APLET key is used to list all the aplets and to , or

The

them.

SYMB view is used to enter equations….

The It can store up to ten functions. If you copies of the aplet then any number of functions can be used.

NUM view shows the function in table form…

The

additional

The

PLOT view is used to display the function as a graph…

At the bottom of the

PLOT view is the

key. This gives access to a number of other useful tools allowing further analysis of the function. Some of these tools have their own sub-menus.

PLOT SETUP view controls the settings for the PLOT view…

The

NUM SETUP view controls the settings for the NUM table view…

The

Although these views are superficially different in other aplets, the basic idea is usually similar.

Having said that aplets are best thought of as “working environments”, it is equally true that aplets are essentially programs, with the standard ones simply being built into the calculator. This is a programmable calculator, having its own programming language and able to perform quite sophisticated tasks.

Unless you particularly want to learn about the programming language, there is no reason why you should worry about it. The standard aplets will cover all of your normal requirements in mathematics.

However one of the great strengths of the hp 39gs and hp 40gs is their ability to “download” additional aplets from other calculators and from the Internet. See page

245.

A mini-USB cable (see page 237) and software were provided with your hp 39gs and hp 40gs which you

A g

can use to connect your PC to your calculator via the USB port and then download aplets from the computer to the calculator or to save your work to the computer. If you have an earlier model such as the hp 38g, hp 39g or hp 40g then you need to buy the cable separately from an HP reseller and download the software from Hewlett-Packard’s website. More information on this can be found on pages 245 - 274.

Calculator Tip

If you search on the web using the key words “39g” or “40g” and you will find a variety of sites which contain information and aplets. lar

e variety of programs and aplets were written for the older hp 39g & hp 40g and these will generally run with no problems on the hp 39gs & hp 40gs. www.hphomeview.com) has the largest

The author’s site (

collection and has extensive help pages as well.

Once an aplet is transferred onto any calculator from the PC, transferring it to another takes only seconds using the built in infra-red link at the top of each calculator on the hp 39gs or using the mini-serial cable on the hp 40gs. The infra-red link is exactly like the remote control of a TV or VCR, and allows two calculators to talk to each other. In the interests of security in examinations the distance over which the infra-red link can communicate is limited to about 8 - 10cm (about 3 - 4 inches). See page

237 for details on this process. The hp 40gs does not have infra-red because some of the markets for which it was produced did not wish students to have this capability.

Aplets are available to do many mathematical tasks such as statistical simulations, time series analysis as well as many tasks called for in calculus, physics and chemistry. There are a number of sites which offer aplets.

The Hewlett-Packard site is found at…

http://www.hp.com/calculators

(follow the links to graphical calculators and then your model)

In addition to this you should check the site called The HP HOME view which can be found at…

http://www.hphomeview.com

(This site is maintained by the author and contains not only hundreds of aplets and games, but also a huge amount of detailed information on the 39gs/40gs family of calculators.)

The entire topic of aplets is discussed in more detail in the chapter entitled “Copying & creating aplets” on page

226.

Calculator Tip

The aplets for an hp 39/40 family are interchangeab e but those of an hp 38g are not.

If you load an aplet from an hp 38g onto an newer

model then the download may appear to be successfu but the

calcu ator will “crash” when the aplet is run. No permanent damage

will be done but it may cause a reset with loss of user information. Programs from the hp 48 and 49 family are not compatible with those of the 39/40 family (nor vice versa).

HHE

HHOOMME

In addition to the aplets, there is also the scratch pad for all the others. This is accessed via the you will do your routine calculations such as working out 5% of $85, or finding √35. The

HOME view is the view that you will most often use, so we will explore that view first.

WWhhaattiisstthheeHHOOMMEEvviieeww?

This is the accessed from it and can affect it to varying degrees. All mathematical functions are available in this view. You should learn to use this view as efficiently as possible, since a great deal of work will be done here.

We will explore the

HOME base for the calculator. All other aplets can be

HOME view in the following order:

• Exploring the Keyboard

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HOME view, which can best be thought of as a

HOME key and is the view in which

• Angle and numeric settings

• Memory management

• Fractions on the hp 39gs & hp 40gs

• The

• Storing and retrieving memories

• Referring to other aplets from the

• An introduction to the

• Resetting the calculator

HOME History

HOME view

MATH menu

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The first step in efficient use of the calculator is to familiarize yourself with the mathematical functions available on the keyboard. If we examine them row by row, you will see that they tend to fall into two categories - those which are specific to the use of aplets, and those which are commonly used in mathematical calculations.

The screen keys

The first row of blank keys are context defined. The reason they have no label is that their meaning is redefined in different situations - they are the ‘screen keys’. The current meaning of each key is listed in the row of boxes at the bottom of the screen.

A common abbreviation used for these keys is “screen key 1” ). In the are labeled, such as the row of screen keys labels in the another view where all the keys are in use, change to the

Aplet related keys

The next two rows of keys and part of the third are mainly aplet related, so we’ll deal with them as a group.

The arrow keys

The arrow keys on the right are used in most views, usually to move the cursor (a small cross) or the highlight around on the screen.

PLOT view shown right, some of the screen keys

key. When you press this key the

PLOT view appear or disappear. To see

Calculator Tip

Develop the habit of checking the screen to see if any of those keys have been given meanings. In many views, the screen keys have been set up with useful shortcuts and functions.

SK1 or SK2 etc (for

APLET view.

The

APLET key is used to choose between the various different aplets

available. Everything in the calculator revolves around aplets, which you can think of either as miniature programs or as environments within which you can work.

The hp 39gs and hp 40gs come with twelve standard aplets - Finance, Function, Inference, Parametric, Polar, Linear Solver, Triangle Solver, Quadratic Explorer, Sequence, Solve, Statistics and Trig Explorer. Which one you want to work with is chosen via the page

14 for more details on this.

APLET key. See

Calculator Tip

The name of the active aplet is shown at the top of the screen, as above. It is important to bear this in mind because the angle and numeric settings are tied to the active aplet. Changing aplets may therefore cause these settings to change in

HOME too. See page 28.

In addition to the standard twelve, covered in great detail in the chapters following, many more aplets are available from the Internet written by other programmers. Once these are downloaded into your calculator they can also be accessed via the

APLET key. For more detail on this type of aplet, see the brief summary

later in this section, and the chapter entitled “Programming the hp 39gs & hp 40gs” on page 255.

The SYMB, PLOT and NUM keys

When working mathematically there are three ways that we view functions:

• symbolically, as an equation;

• numerically, as a table;

• graphically, as a graph in various formats.

SYMB, PLOT and NUM keys are intended to reflect this common

The methodology. In most aplets the

SYMB view shows the equations and the NUM view shows the

PLOT view shows the graph, the

equations in tabular (numeric) format.

The VIEWS key pops up a menu from which you can choose various options. Part of the See page

85 for more detailed information. A summary only is given

VIEWS menu for the Function aplet is shown right.

below.

Essentially the

VIEWS menu is provided for two purposes…

Intro to the VIEWS menu

Firstly, within the standard aplets (Function, Sequence, Solve etc.) it provides a list of special views available to enhance the

For example the standard covering the whole screen, but the screen such as shown right. Information on the

PLOT view.

PLOT screen provides a standard graph

VIEWS menu lets you use a split

VIEWS menu is given in

the chapter dealing with the Function aplet.

In its second role, the

VIEWS key also has a critical purpose when using aplets which have been downloaded

from the Internet. When a programmed aplet is created for the hp 39gs or hp 40gs, a menu is provided by the programmer to let you control and use it. During the programming this menu is tied to the

VIEWS key,

replacing the menu normally found on the key.

For example, the snapshot shown right is of a

VIEWS menu taken from

an aplet designed to analyze and graph Time Series data.

The next important key is the

HOME view from wherever you are. Above it is the MODES key,

the accessed by pressing

SHIFT first. More detailed information on these

HOME key. It allows you to change into

two views follows later.

The VARS key

VARS key is used, mainly by programmers, as a compact way to access all the

The different variables stored by the calculator including aplet environment variables.

Shown right are two views of the list showing the graphic variables (memories) from the

PLOT.

The

APLET list showing some of the variables in the set controlling

VARS key is not generally used much, and you may not have

VARS screen, the first from the HOME

G1, G2…. and the next

followed this explanation. This is not important as it is a key that is very rarely used by the average user. A few uses for the average user are detailed in the Function aplet’s “Expert User” section on page 62.

MATH key next to VARS is far more important and provides access to a

The huge library of mathematical functions. The more common functions have keys of their own, but there is a limit to the number of keys that one can put on a calculator before it takes too long to find the key required. Hence the

MATH menu lists all those functions that would not fit onto the

The

MATH key.

keyboard plus some which also appear on the keyboard. Shown in the screen snapshot right is a small selection of the total list. For a listing of almost all the functions, with examples of their use, see the chapter entitled “The MATH Menus” on page 165.

As is usual with all calculators, most of the keys have another function above the key. The hp 39gs and hp 40gs get twice the action from each key by having this second function.

The second function is accessed via the

SHIFT key on the left side of the calculator. Although this book will

sometimes tell you explicitly to press this key, in most cases it will be assumed that you are intelligent enough to work out for yourself when it is necessary to press it.

The

ALPHA key gives access to the alphabetical characters, shown below and

right of most keys. Pressing

SHIFT ALPHA gives lower case.

Calculator Tip

If you press and hold down the key you can ‘lock’ alpha mode,

ALPHA

although this doesn’t work for lower case. Many people use this to type in functions by hand rather than going through the views, such as the Notepad, also offer a screen key function that lets you lock either upper or lower case alpha mode.

The SETUP views

SETUP views, above PLOT, SYMB and NUM, are used to customize

The their respective views. For example, the

PLOT SETUP screen controls things

like axes, labels etc. Their use changes in different aplets, so for more information see the explanations in the chapters dealing with the various aplets, particularly in the Function aplet on page

50.

MATH

menu. Some

SYMB SETUP key is only used in one place, which is to choose the data model for bivariate statistics in

The the Statistics aplet. It is not available in the other aplets and trying to access it will result only in a quick flash of an exclamation mark on the screen to say “You’ve done something wrong!”.

Information on the use of the

VIEWS keys) can be found in the chapters “Working with Sketches” and

and

SKETCH and NOTE views (located above the APLET

“Working with Notes & the Notepad” on pages 222 & 217.

The main use for the

SKETCH and NOTE views is in aplets downloaded from the Internet. Instructions for

using the aplet are sometimes included with the aplet in note form, and sometimes as an accompanying sketch.

The MODES view

The

MODES view (see right) controls the numeric format used in

displaying numbers and angles in aplets. At the bottom of the screen you will see that one of the screen keys has been given the function

. Pressing this key pops up a menu of choices from which you can select the option which suits you. The default angle setting is radians.

Calculator Tip

If you don’t want to use the menu then, rather than pressing highlight the field and then press the ‘ ’ key repeatedly. This will cycle

through the choices without popping up a menu. This can be much faster if the menu has only a few choices.

Numeric formats

The choices for ‘

Number format’ are shown on the right. Standard is

probably the best choice in most cases, although it can be a little annoying to constantly have 12 significant figures displayed. In

Standard mode, very large and very small numbers are displayed in

scientific notation.

Fixed, Scientific and Engineering formats all require you to

The specify how many decimal places to display. The screenshot right shows

Fixed 4, which rounds everything off to 4 decimal places. Of course,

you can change the

A setting of

Scientific ensures that any results are displayed in scientific notation. Of course, the

4 to any other number you want.

calculator’s idea of scientific notation may not be the same as yours. Since the calculator has no way of displaying powers as superscripts, a result of

Engineering is very similar to Scientific, except that powers are displayed as multiples of 3 (ie. 10 ,10

3203 ×10

has to be displayed as 3.203E4. The alternative of ⋅

This is done to allow easy conversion in the metric system, which also works in multiples of 1000.

The screens right show the same two numbers displayed as in turn as;

Engineering 4.

Fixed 4, Scientific 4 and

Calculator Tip

If you have Labels turned on when you in (or out) on a graph or choose a Trig scale then you may end up with axes whose numeric labels are horrible decimals (see below right).

The setting of in more detail on page

The next alternative in the

Fraction can be quite deceptive to use and is discussed

33.

MODES view of Decimal Mark controls the character which is used as a decimal

point. In some countries a comma is used instead of a decimal point.

If you opt to use a comma rather than a full stop then any places where a comma would normally be used (such as in lists) will swap to using a full stop. Any functions which might normally have terms separated by a comma will use a full stop instead. For example, become

ROUND(3,456.2).

ROUND(3.456,2) will

Moving back to our tour of the keyboard, the next key is

ENTER key. This is used as an all purpose “I’ve

the finished - do your thing!” signal to the calculator. In situations where you woul

ators, press the

calcul

key. This can be used to retrieve the final value of the last

ANS

d normally press the ‘

ENTER key instead.

=’ key on most

Above the

ENTER key is the

calculation done. An example is shown right.

The ANS key

−

If you are not confident about using brackets, then the ANS key can be quite useful.

372

For example, you could calculate the value of

2 5

by using

brackets…

…. or you could use the ANS key.

A better alternative to using the the

function. This is discussed on page 37.

ANS key is to use the History facility and

The negative key

Another important key is the

(-) key shown left. It is important to realize that the

hp 39gs and hp 40gs do not treat a negative as being the same as a subtract.

If you want to calculate the value of (say)

−−2(9) then you must use the (-) key

before the 2 and the 9 rather than the subtract key. If you press the subtract key twice, entering ‘subtract, subtract 9’ instead of ‘subtract (-) 9’ you will receive an error message of “Invalid syntax”, meaning it does not make mathematical sense to have two subtract signs rather than a subtract of a negative.

Similarly, if you press ‘subtract 2’ as the first keys in the above calculation then the calculator will display

Ans - 2. The reason for this is that a subtract cannot start an expression in mathematics, while a negative

sign can. Since the subtract can’t come first, the calculator decides that you must have intended to subtract from the previous answer. Hence the sudden appearance of an common error by new users is to enter a value into the

PLOT SETUP view using subtract instead of negative.

Ans. This occurs at other times too. A

This will usually have unexpected results.

The CHARS key

The next important key is the

VARS). It accesses a view containing the characters

CHARS key (above

that are required occasionally but not often enough to bother putting on the keyboard.

Pressing the screen keys is set to be a ‘Page Down’ key

SHIFT CHARS will pop up the screens shown right. One of

, and will give

access to two more pages of characters as shown.

These special characters are obtained by pressing the screen key labeled

. You can press as many times as you need to in order to obtain multiple characters. When you have as many as you need, press the

is not required – just press

key. If you only require one character then

The DEL and CLEAR keys

Another important key is the

DEL key at the top right of the keyboard. This serves as a

backspace key when typing in formulas or calculations, erasing the last character typed. If you have used the left/right arrow keys to move around within a line of typing, then the

DEL key will delete the character at the cursor position.

CLEAR key above DEL can be thought of as a kind of ‘super delete’ key. For example, if pressing DEL

The would erase one function only in the

SYMB view then CLEAR will erase the whole set.

Calculator Tip

Another use for the DEL For example, if you move back into the screen and change to Degree mode, then pressi DEL lt of Radians. Pressing

CLEAR in the MODES view would restore factory settings to all the

ng the key will restore the defau

entries. This is particularly useful in the

key is to restore factory settings.

MODES

PLOT SETUP

view.

The remaining keys of chapters of their own.

LIST, MATRIX, MEMORY, NOTEPAD and PROGRAM have special

AAnngglleeaannddNNuummeerriiccsseettttiinnggs

It is critical to your efficient use of the hp 39gs and hp 40gs that you understand how the angle and numeric settings work. For those few who may be upgrading from the original hp 38g released in the mid ‘90s this is particularly important, since the behavior is significantly different.

On the hp 39gs and hp 40gs, when you set the angle measure or the numeric format in the applies both to the aplet and to the aplet (the one highlighted in the

HOME view. However, this setting applies only to the currently active

APLET view).

This means that if you change active aplet then these settings may change also, not only for the aplet but in the

HOME view too.

For example, suppose you have been performing trig calculations in the

HOME view with the Function aplet being currently active, and have set

the angle measure to

DEG.

If you were to now change to the Solve aplet in order to solve an equation then the settings would revert to those of the Solve aplet; probably be radians unless you had also changed those as well.

Radian measure is the default for all aplets and thus also for unless you change it. Performing exactly the same calculation in

HOME

would now give a different result, as shown right.

MODES view, it

Although this may seem to be a strange way of doing things, there is actually a very good reason for it. On the original first model, the hp 38g, the settings for the

HOME view were independent from those of the aplets

and it caused a number of users to have difficulties as you'll see on the next page.

Suppose we define a trig function in the

Function aplet as shown.

The default setting for the Function aplet is radians, so if we set the axes to extend from -

to π, the graph would

look as shown right.

PLOT

In the

view shown, the first positive root has been

found (see page 57) as x=1.0471…

On the hp 39gs and hp 40g, if we now change to the retrieve the root and perform the calcul

ation shown right, we expect that

the answer should be zero, as indeed it is.

HOME

view,

However, this is only the case because the angle measures of problem was that on the original hp 38g the default setting for the Function aplet was radians, while

HOME and the Function aplet agree. The

HOME

had a default setting of degrees and its setting was independent of those of the aplet. This meant that a calculation such as the one above would give incorrect results, and caused considerable confusion to some students. It even resulted in users returning their hp 38g to dealers as being ‘faulty’! Hence the change, which was first made in the hp 39g and hp 40g.

The only drawback of synchronizing the settings of the

HOME and aplet

is that you might change aplets and forget that it may also change the

HOME view settings. For this reason, the name of the active aplet is

shown at the top of the

HOME view as a reminder.

On the hp 39gs and hp 40gs you can see that if we turn

Labels on and then PLOT,

the numeric mode also affects the axis labels.

The default behavior in the

PLOT view is to not display axis labels due

to the way that they often interfere with the clear display of the graph.

Settings made in the

SHOW command, covered on page 38.

MODES view also apply to the appearance of equations and results displayed using the

Calculator Tip

Under the system used on the hp 39gs and hp 40gs, if you want to work in degrees then you will need to choose that setting in the MODES view and possibly set it again if you change to another aplet. Some people choose to go through and change the setting on all the aplets at once so that they don’t have to remember that it might change. However, if you an aplet or reset the calculator then the default setting will return.

MMeemmoorryyMMaannaaggeemmeennt

One of the major complaints about the original hp 38g was its memory - mainly the lack of it at only 23Kb, but also the inability to easily control or manage it. This problem has been addressed on the hp 39gs and hp 40gs in two ways. Both have a very ample amount, just short of 200Kb, and there are very few users who will come close to filling this. Depending on size, there is enough room for at least 40 aplets, 40 pages of notes, or nearly 10,000 data points although not, of course, all at once.

The MEMORY MANAGER view

In addition to all this memory, the hp 39gs and hp 40gs supply an easy way to control it through the

MEMORY key you will see the view shown right. Scrolling through it

the will show you exactly how the available memory is currently being used. The remaining memory, in Kb, is shown at the top right of the screen. This view gives an overview of the memory. For detailed management the

Pressing you can delete entries no longer needed.

key is provided.

on any entry will take you a relevent screen in which

MEMORY MANAGER view. If you press

For example, with the highlight on Aplets, pressing

APLET view (right), where you can choose to delete or reset any

to the aplets no longer required.

will take you

+ 336 hidden pages