A Crash Course in Mathematica [Kaufmann 1999-07-30].pdf

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Stephan Kaufmann
Crash Cou rse
in
Mathematica
Birkhauser Verlag
Basel· Boston · Berlin
Author:
Stephan Kaufmann
Mechanik
ETH
Zentrum
CH-8092 Zurich
E-mail: kaufmann@ifm.mavt.ethz.ch
Homepage: http://www.ifm.ethz.ch/- kaufmann
1991 Mathematics Subject Classification 00-01
A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA
Deutsche Bibliothek Cataloging-in-Publication Data
A
Crash Course in Mathematica
[Medienkombinationl
I
Stephan
Kaufmann. - Basel; Boston; Berlin: Birkhauser
ISBN
978-3-7643-6127-3
ISBN
978-3-0348-7589-9
(eBook)
DOI 10.1007/978-3-0348-7589-9
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is con-
cerned, specifically the rights of translation, reprinting, re-use of illustrations, broadcasting, reproduction
on microfilms or in other ways, and storage in data banks. For any kind of use whatsoever, permission
from the copyright owner must be obtained.
The software and hardware terms referred to in this book are in most cases also registered trademarks
and as such come under the same legal restrictions. The text, illustrations and programs have been
carefully prepared. However, the publisher and the author accept no responsibility for errors or their
consequences.
Mathematica®
is a registered trademark of Wolfram Research, Inc.
MathReader®
ist a registered trademark of Wolfram Research, Inc.
©1999 Birkhauser Verlag, Postfach 133, CH-4010 Basel, Schweiz
Cover design: Markus Etterich, Basel
Printed on acid-free paper produced of chlorine-free pulp. TCF
oc
987654321
• Contents
Preface ..............................................................................................................................
A Short Tour .....................................................................................................................
Formula Entry ...........................................................................................................
Numerical Calculations ............................................................................................
Symbolic Mathematics ..... ... ... .......... ............ ....... ... ... ....... ....... ....... ... ....... ................
Graphics ....................................................................................................................
Programming ... ..... ..... ... ..... ... ... ............ .......... ..... ... ....... ............... ... ..... .....................
Some of the Most Important Functions ....... ..... ... ..................... ... ..... ..................... ...
Part 1: The Basics
...........................................................................................................
1.1 The Structure of the Program. ... ............................. .............. ..... ...................... ...
1.1.1 The Front End ..........................................................................................
1.1.2 The Kernel ...............................................................................................
1.2 Online Documentation .. ....... .............................. ....................... ....... ......... .........
1.3 Formulas .............................................................................................................
1.3.1 Formats ....................................................................................................
1.3.2 Entering Formulas and Special Characters .............................................
1.4 Simple Calculations ............................................................................................
1.4.1 Conventions .............................................................................................
1.4.2 Numerical Calculations ...........................................................................
1.4.3 Algebraic Manipulation ... ... ... ... .......... .......... ...... ............. ........................
1.4.4 Transformation Rules and Definitions ....................................................
1.4.5 Equations .. .......................... ..... ...................... ........ .................... ....... ... ....
1.4.6 Calculus .... .................... ...... ..... ............... .... ... ..... ... ........................ ... .......
Part 2: Graphics
.... ............ ... ............. ..... ..... ....................... ............................ ....... .........
2.1 Graphs of Functions of One Variable............ ....... ... ... ........... ... ........ ... ... ............
2.2 Graphs of Functions of Two Variables .......................................... ....................
2.2.1 Surfaces ... .............. ....... ....... ............................ ..... ...... ....... ..... ... ..............
2.2.2 Contours ..................................................................................................
2.2.3 Density Plots.... ..... .... ... ... ......... ..... ........ ... ... ......... ............ .................... ....
2.3 Parametric Plots ..................................................................................................
2.3.1 Two-Dimensional Parametric Plots .........................................................
2.3.2 Three-Dimensional Parametric Plots .......................................................
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2.4 Tools from Standard Packages ........................................................................... 100
2.4.1 Three-Dimensional Contour Plots ........................................................... 100
2.4.2 Tools for Two-Dimensional Graphics ..................................................... 101
6
2.4.3 Tools for Three-Dimensional Graphics ................................................... 102
2.4.4 Legends ................................................................................................... 103
2.4.5 Vector Fields ........................................................................................... 105
2.5 Animations ......................................................................................................... 110
2.6 Exporting to Other Programs ............................................................................. 113
Part 3: Lists and Graphics Programming
.................................................................... 115
3.1Lists .................................................................................................................... 116
3.1.1 Creating One-Dimensional Lists ............................................................. 116
3.1.2 Manipulating Lists ................................................................................... 117
3.1.3 Multidimensional Lists ............................................................................ 120
3.2 Calculating with Lists ......................................................................................... 120
3.2.1 Automatic Operations .............................................................................. 120
3.2.2 Mapping Functions on Lists ................................................................... .121
3.2.3 Pure Functions ......................................................................................... 122
3.2.4 Using List Elements as Arguments ......................................................... 124
3.2.5 Plotting Lists ............................................................................................ 126
3.3 Linear Algebra .................................................................................................... 131
3.4 Graphics Programming ....................................................................................... 136
3.4.1
Graphics
Objects ................................................................................. 136
3.4.2
Graphics3D
Objects ............................................................................. 139
3.4.3 Objects from Standard Packages ............................................................ .140
3.5 Application: Animating a Mechanism ............................................................... 146
Part 4: Introduction to Programming
.......................................................................... 151
4.1 Expressions ......................................................................................................... 152
4.2 Patterns ............................................................................................................... 155
4.2.1 Simple Patterns ........................................................................................ 155
4.2.2 Constraints ............................................................................................... 157
4.2.3 More Complicated Patterns ..................................................................... 162
4.2.4 A Simple Integrator ................................................................................. 163
4.3 Evaluation ........................................................................................................... 167
4.3.1 Associated Definitions ............................................................................ 167
4.3.2 Attributes ................................................................................................. 168
4.3.3 The Evaluation Process ........................................................................... 169
4.4 Programming Tools ............................................................................................ 172
4.4.1 Local Variables ........................................................................................ 172
4.4.2 Functional Programming ......................................................................... 173
4.4.3 Rule-Based and Recursive Programming ................................................ 176
4.4.4 Procedural Programming ......................................................................... 179

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