The Maple® O.D.E. Lab Book

167 Pages·1996·4.18 MB·English

by  Darren Redfern

The Maple® O.D.E.
Lab Book
Springer
New York
Berlin
Heidelberg
Barcelona
Budapest
Hong Kong
London
Milan
Paris
Santa Clara
Singapore
Tokyo
Darren Redfern Edgar Chandler
The Maple®
O.D.E. Lab Book
With 50 Figures
DOS Diskette Included
Springer
Darren Redfern Edgar Chandler
Practical Approach Corporation Scottsdale Community College
151 Frobisher Drive, Suite C-210 9000 E. Chaparral Road
Waterloo, ON N2V 2C5 Scottsdale, AZ 85250
Canada USA
Library of Congress Cataloging-in-Publication Data
Redfern, Darren.
Maple® O.D.E. lab book/Darren Redfern, Edgar Chandler.
p. cm.
Includes bibliographical references and index.
1. Differential equations-Numerical solutions-Data processing.
2. Maple (Computer file) I. Chandler, Edgar. II. Title.
QA371.5.D37R43 1996
515'.352'078-dc20 96-19514
Maple is a registered trademark of Waterloo Maple, Inc.
Printed on acid-free paper.
© 1996 Springer-Verlag New York, Inc.
Softcover reprint of the hardcover 1s t edition 1996
All rights reserved. This work may not be translated or copied in whole or in part without the
written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New
York, NY 10010, USA), except for brief excerpts in connection with reviews or scholarly
analysis. Use in connection with any form of information storage and retrieval, electronic
adaptation, computer software, or by similar or dissimilar methodology now known or
hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this publication,
even if the former are not especially identified, is not to be taken as a sign that such names,
as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used
freely by anyone.
Production managed by Frank Ganz; manufacturing supervised by Jacqui Ashri.
Photocomposed copy prepared from the authors' "0-TEX files.
987654321
ISBN-13: 978-0-387-94733-4 e-ISBN-13: 978-1-4612-2402-0
DOl: 10.1007/978-1-4612-2402-0
We would like to gratefully dedicate this project to our families and
colleagues who, over the years, have been very supportive and helpful,
providing much appreciated guidance and direction.
Contents
1. Introduction 1
How This Lab Book Is Organized 2 • Using the
Diskette 2 • Where to Go for More Information 3 •
Acknowledgments 3
2. Getting Started with Maple 4
Starting Maple 4 • Basic Maple Syntax 5 •
Basic Maple Objects 8 • Mixing and Matching
Different Number Types 9 • Strings 10 • Maple
Expressions 11 • Sets and Lists 13 • Calling Maple
Commands 16 • Assignments and Equations 19 •
The Use of Quotes in Maple 22 • Activities for §2 23
3. First-Order ODEs 25
Defining and Solving First-Order ODEs 25 • Explicit vs.
Implicit Solutions 28 • Activities for §3 31
4. Applications of First-Order ODEs 33
Falling, Floating, or Accelerating Objects 33 • Mixture
Problems 40 • Activities for §4 42
vii
viii • Contents
5. Graphical Methods 45
Direction Fields 46 • Some Examples 49 • Activities
for §5 53
6. Homogeneous Linear Differential Equations 56
Activities for § 6 63
7. Non-homogeneous Linear Differential Equations 65
Activities for §7 69
8. Applications of Linear Differential Equations 71
Free, Undamped Motion 72 • Free, Damped
Motion 75 • Activities for § 8 81
9. More Applications and Systems of Differential Equations 83
Forced Motion 83 • Systems of Linear Differential
Equations 87 • Activities for §9 89
10. Phase Planes 91
Activities for § 10 98
11. Matrix Operations 100
Basic Concepts 100 • Characteristic Values and
Characteristic Vectors 106 • Activities for §11 109
12. Matrix Methods of Solution 111
Activities for § 12 116
13. Isoclines 117
Activities for § 13 119
14. Series Solutions 121
Activities for § 14 129
Contents • ix
15. Numerical Methods 131
Problems with Numerical Methods 136 • Activities for
§15 139
16. The Laplace Transform 140
Activities for §16 152
Bibliography 154
Index 157
CHAPTER Introduction
The Maple ODE Lab Book is intended to provide a thorough introduc
tion to using symbolic computation software to model, solve, explore, and
visualize ordinary differential equations. It is best used as a supplement to
existing texts (see the bibliography for some of our recommended texts).
Maple was chosen as our software package because of its ease-of-use,
affordability, and popularity at many universities and colleges around the
world. The version being used is Maple V Release 4. If you have a previous
release of Maple, some of the commands shown in this lab book will work
differently (or not at all), but the basic groundwork for solving ODEs hasn't
changed. Speak to your system administrator about upgrading to Release
4, or contact:
Waterloo Maple Inc.
450 Phillip Street
Waterloo, Ontario
CANADA N2L 5J2
Phone: [phone]
FAX: [phone]
E-mail: [email protected]
WWW: http://www.maplesoft.com
1
2 • Chapter 1. Introduction
How This Lab Book Is Organized
Each subsequent chapter of this lab book contains information and ex
amples of how to apply Maple to various elements of ordinary differential
equations. It is suggested that you read the chapters with your computer on
and Maple V Release 4 running. You can then execute many of the com
mands yourself and experiment by changing various parameters and/or
initial conditions, observing the corresponding changes in the results.
At the end of each chapter, a set of exercises is provided for the reader
to complete. Maple worksheets containing answers to all exercises (and
other valuable information) can be found on the diskette at the back of the
lab book.
U sing the Diskette
This lab book comes with a single DOS-formatted diskette, which contains
the following files:
• 15 worksheets, named chap2.mws through chap16.mws. Each work
sheet contains answers to the corresponding exercises in the lab book,
as well as an experimentation section that approaches some of the ma
terial from that chapter in a slightly different way than in the book.
• The files chart.mws and chart.m. These files contain the code for a
utility procedure (printchart) created in Chapter 4. Have your system
administrator place chart.m in a directory easily accessible by your
copy of Maple.
All files on this diskette should work on any computer platform that
Maple V Release 4 supports. If you are not on a DOS (i.e., Windows) based
machine, you should be able to transfer the contents of a DOS diskette onto
your system (for example, with the Mac utility AppleFileExchange).
If you cannot transfer the files, contact your system administrator. If
that fails, please contact us at one of the addresses listed in the next section.
Ground Mail: Practical Approach Corporation
151 Frobisher Drive, Suite C-210
Waterloo, Ontario
CANADA N2V 2C5