Mastering the hp 39gs & hp 40gs

[Pages:366]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

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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.

? Copyright 2006 Hewlett-Packard Development Company, L.P.

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

2 INTRODUCTION

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.

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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 .

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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