Practical Use of Mathcad®: Solving Mathematical Problems with a Computer Algebra System

518 Pages·1999·21.92 MB·English

by  Prof. Dr. Hans Benker (auth.)

Practical Use
ofMathca~
Springer-Verlag London Ltd.
Hans Benker
Practical Use
of Mathcad®
Solving Mathematical Problems with a Computer Algebra System
Translated by Anthony Rudd
, Springer
Prof. Dr. Hans Benker
Martin-Luther-Universităt
Fachbereich Mathematik und Informatik
06120 Halle (Saale)
Germany
British Library Cataloguing in Publication Data
Benker, Hans
Practica1 use ofMATHCAD : solving mathematical problems
With a computer algebra system
1. Mathcad (Computer file) 2. Mathematics - Computer programs
1. Title
510.2'85'5369
Library of Congress Cataloging-in-Publication Data
Benker. Hans, 1942-
[Mathematik mit MA THCAD. English]
Practical use of MA THCAD : solving mathematical problems with a
computer algebra system / Hans Benker : Translated by Anthony Rudd.
p. cm.
Revised, extended edition of the original German title "Mathematik
mitMATHCAD".
Includes index.
ISBN 978-1-85233-166-5 ISBN 978-1-4471-0539-8 (eBook)
DOI 10.1007/978-1-4471-0539-8
1. Mathematics-Data processing. 2. MathCAD. 1. Title.
QA76.95.B4613 1999 99-33922
51O'.0285'5369-dc21 CIP
Apart from any fair dea1ing for the purposes of research or private study. or criticism or review. as
permitted under the Copyright, Designs and Patents Act 1988. this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the
publishers, or in the case of reprographic reproduction in accordance with the terms of licences issued
by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be
sent to the publishers.
© Springer-Verlag London 1999
Originally published by Springer-Verlag London Limited in 1999
Origina1ly published in German under the title Mathematik mit Mathcad 2nd edition by Hans Benker
The use of registered names, trademarks etc. in this publication does not imply, even in the absence of a
specific statement, that such names are exempt from the relevant laws and regulations and therefore free
for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the
information contained in this book and cannot accept any legal responsibility or liability for any errors
or omissions that may be made.
Typesetting: Camera ready by author
34/3830-543210 Printed on acid-free paper SPIN 10836071
For my wife Doris
and my daughter Uta
Preface
This book, which is a rrMsion and extension of the original edition publi
shed in 1996 (see [2D with the German title Mathematik mit MA'nfCAD
(Mathematics Using MA'nfCAD), discusses the use of the program system
MAlHCAD® to solve mathematical problems with computers. The book is
based on the current MA'nfCAD Version 8 Professional for WINDOWS
95/98 (see [5D.
Whereas MAlHCAD and MATLAB (see [4D were originally conceived as
purely systems for numerical mathematical calculations, the more recent
versions of both products have licensed a minimum variant of the symbolic
processor of the MAPLE computer algebra system for exact (symbolic) calcu
lations.
Thus, MAlHCAD has been developed to be an equal partner to the estab
lished computer algebra systems AXIOM, DERIVE, MACSYMA, MAPLE, MA
lHEMATICA, MuPAD and REDUCE. However, because these systems con
tain numerical methods as well, they are no longer just pure computer alge
bra systems.
Consequently, MAlHCAD can also be deSignated as being a computer alge
bra system (or just: system).
MATHCAD possesses some advantages:
• Better numerical capabilities more than compensate for the somewhat
limited capabilities provided for exact (symbolic) calculations.
• The calculations are performed in the MAlHCAD worksheet using the
usual mathematical symbols (standard notation).
• Thanks to the superior layout capabilities in the worksheet, MAlHCAD
can be used to create treatises directly.
• All calculations can be performed using units of measurement.
• The more than 50 electronic books that exist for various mathematical,
technical, scientific and economics disciplines contain all the standard
formulae, equations and mathematical methods relevant for the subject.
Detailed text and graphics explain these entries, which can be integrated
without difficulty into your own calculations.
These advantages have been a Significant factor in making MAlHCAD one
of the preferred systems for engineers and scientists.
MAlHCAD exists for various computer platforms, such as for IBM-compa
tible personal computers, workstations under UNIX and APPLE computers.
viii Preface
We have used for this book the Vernon 8 Professional for IBM-compatible
personal computers with a Pentium processor (generally referred to as PCS)
running under WINDOWS 95/98. Because the form of the user inteiface and
the menu and command structure does not significantly differ for other
types of computer, the discussions made in this book are generally applica
ble.
Because the user interface for Version 8 described in the book has changed
only slightly from Version 7, most of the problems discussed in the book
can also be calculated using Version 7. The same applies for Versions 5 and
6. The author's previous books [2,3,4] contain additional details. However,
all earlier versions have reduced capabilities and have fewer functions than
those supplied with Version 8.
In the author's opinion, the MAlliCAD system has unjustifiably only in the
last few years received the attention it deserves. This makes itself apparent,
for example, in the limited number of books that have been published on
MA1HCAD. This book aims to help close this gap. Its audience addresses
both students and employees at polytechnics and universities, as well as en
gineers and scientists working in industry and institutes.
This book provides solutions to basic mathematical problems for engineer
ing and natural science. It can serve both as reference and tutorial for lec
turers and students as well as a manual for experts.
This book is based on lectures that the author held at Halle University for
students of mathematics, computer science and engineering.
In order to keep the book compact, the mathematical theory of the dis
cussed problems is handled only to the extent needed to produce a solu
tion using MA1HCAD. Consequently, all proofs have been omitted. How
ever, this does not mean that mathematical rigour is ignored, as is the case
in many books concerned with computer algebra systems.
This book focuses on transforming the basic mathematical problems that are
to be solved into the language of MAlliCAD and on the interpretation of
the returned results. To save the reader from tedious searching to fmd the
solution to a problem, value is placed on a concise description.
If the readers have mathematical difficulties, they should consult the ap
propriate mathematical books (see Bibliography).
This book is divided into two parts:
I. Chapters 1 - 11 :
Introduction: Preface, installation, structure, user interface and basic
properties of MA1HCAD
II. Chapters 12 - 27 :
Main part: Solution of mathematical problems from engineering and
natural science using MAlliCAD
The copious examples that illustrate all the discussed mathematical prob
lems should be used as exercises. These examples show the reader the ca
pabilities and limitations involved with the use of MA1HCAD.
Preface
Because computers on which computer algebra systems have been installed
will replace hand-held calculators, the use of such systems to solve mathe
matical problems using computers will gain in importance in future.
Because these systems can be used without requiring extensive program
ming and computer knowledge, and can solve most of the standard
mathematical problems, their role will increase for the user. Before you use
or write software in a conventional programming language such as BASIC,
C, FORTRAN or PASCAL, because it is much simpler to solve the problem
using an available computer algebra system, you will try this approach ftrst.
Only when this approach fails will you need to return to using numerical
software.
This book shows how MATHCAD as a computer algebra system can be used
to easily solve many mathematical problems. The capabilities of an exact
solution are tried ftrst before an attempt is made to use the numerical solu
tion. This approach is warranted because the MATHCAD system represents a
successful mix of computer algebra methods and numerical methods under
a common WINDOWS user interface. This user intet/ace permits interactive
work and provides a clear display of the calculations.
The author hopes that this introduction to MATHCAD stimulates the readers
not only to make use of MATHCAD to obtain a quick solution to their
problems, but also to consider the mathematical background.
As with all computer algebra systems, MATHCAD cannot replace mathemat
ics. However, it can relieve the user from making long-winded calculations
and avoid computational errors, and so provide the user with time to con
sider the creative use of mathematics.
At this point I would like to thank all those people who supported me in
the realization of this book project:
• Dr. Merkle, Ms. Grunewald-Heller and Ms. Mowat from Springer Verlag
Heidelberg and London for accepting the book suggestion in the pub
lisher's program and for their technical assistance.
• My wife Doris who showed much understanding for my work in the
evenings and weekends.
• My daughter Uta who critically read the manuscript many times and ga
ve many useful suggestions.
• The European branch of MathSoft International in Bagshot (England) for
the free use of the new Version 8 of MATHCAD and the new electronic
books.
Finally, a few comments on the form of this book:
• In addition to headings, MATHCAD functions, commands and me
nus/submenus are shown bold. The same also applies for vectors and
matrices.
• The names of programs, files and directories, and the names of computer
algebra systems are shown in capitals.
x Preface
Examples and figures are numbered starting at 1 in each chapter; the
chapter number is prefixed. Thus, Fig. 2.3 and Example 3.12 represent
figure 3 from Chapter 2 and example 12 from Chapter 3, respectively.
• The symbol
•
is used to indicate the end of an example.
• The symbol
~-
pref1Xes important text passages in the book which are also ended with
the symbol
•
• The symbol
CJ
is used for the space bar.
• Important terms and designations are written italicized. This also applies
for explanatory text for the calculations performed by MAlHCAD that
are taken directly from the MAlHCAD worksheet.
• An => arrow that separates the individual menus of a MAlHCAD menu
sequence also represents a mouse click.
Merseburg, July 1999 Hans Benker
Contents
1 In'troduction. .......................................................................................... 1
1.1 Structure and Operation of Computer Algebra Systems .................. 2
1.2 Application Areas for Computer Algebra Systems .......................... 6
1.3 Development of MATHCAD ............................................................ 11
1.4 Comparison of MATHCAD with other Systems .............................. 13
2 Installation ofMAmCAD• •••••••••••••••.•••••••.•••••••••••••••••••••••••••••••••••••••••• 14
2.1 Program Installation ........................................................................ 14
2.2 MATHCAD Files ............................................................................... 15
2.3 Help System ..................................................................................... 16
2.4 AXUM ............................................................................................... 18
3 MAmCAD User Interface. •.•.•.•..•.•••.•...•.•..•.•••.••.•.•.•.••••••..••••.••.•••••.••.•• 20
3.1 Menu Bar ......................................................................................... 21
3.2 Standard Toolbar. ............................................................................ 23
3.3 Formatting Toolbar .......................................................................... 24
3.4 Math Toolbar. .................................................................................. 24
3.5 Worksheet ........................................................................................ 29
3.6 Status Bar ......................................................................................... 31
4 MAmCAD Worksheet ........................................................................3 2
4.1 Text Arrangement. ........................................................................... 36
4.2 Layout of Calculations ..................................................................... 38
4.3 Worksheets Management. .............................................................. .40
4.3.1 Open, Save and Print ........................................................ .40
4.3.2 Layout ................................................................................. 41
4.3.3 References and Hyperlinks ............................................... .41
4.3.4 Insertion of Objects ........................................................... .43
4.3.5 MathCOnnex ....................................................................... 43
5 mektronic Books. ................................................................................ 44
5.1 Properties, Structure and Handling. ............................................... .45
5.2 Books Available, Extension Packs and Libraries ........................... .50
6 Exact and Numerical Calculations ••••••••••••••••••••••••••••••••••••••••••••••••••••• 54
6.1 Exact Calculation Using Computer Algebra .................................... 57
6.1.1 Symbolic Equal Sign ......................................................... .58
6.1.2 Keywords ...........................................................................6 1
6.2 Numerical Calculations ................................................................... 64
6.3 Control of the Calculation ............................................................... 66
6.3.1 Automatic Mode ................................................................. 67