Advanced Math, Mechanics Applns using MATLAB 3rd ed. - H. Wilson, et al (CRC, 2003) WW.pdf - Matlab - walbo48

Advanced

Mathematics

and Mechanics

Applications Using

M ATLAB ®

Third Edition

Howard B. Wilson

University of Alabama

Louis H. Turcotte

Rose-Hulman Institute of Technology

David Halpern

University of Alabama

CHAPMAN & HALL/CRC

A CRC Press Company

Boca Raton London New York Washington, D.C.

Library of Congress Cataloging-in-Publication Data

Wilson, H.B.

Advanced mathematics and mechanics applications using MATLAB / Howard B.

Wilson, Louis H. Turcotte, David Halpern.—3rd ed.

p. cm.

ISBN 1-58488-262-X

1. MATLAB. 2. Engineering mathematics—Data processing. 3. Mechanics,

Applied—Data processing. I. Turcotte, Louis H. II. Halpern, David. III. Title.

TA345 . W55 2002

620

.00151—dc21

2002071267

This book contains information obtained from authentic and highly regarded sources. Reprinted material

is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable

efforts have been made to publish reliable data and information, but the author and the publisher cannot

assume responsibility for the validity of all materials or for the consequences of their use.

Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic

or mechanical, including photocopying, microﬁlming, and recording, or by any information storage or

retrieval system, without prior permission in writing from the publisher.

The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for

creating new works, or for resale. Speciﬁc permission must be obtained in writing from CRC Press LLC

for such copying.

Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431.

Product or corporate names may be trademarks or registered trademarks, and are

used only for identiﬁcation and explanation, without intent to infringe.

Visit the CRC Press Web site at www.crcpress.com

No claim to original U.S. Government works

International Standard Book Number 1-58488-262-X

Library of Congress Card Number 2002071267

Printed in the United States of America 1 2 3 4 5 6 7 8 9 0

Printed on acid-free paper

′

Trademark Notice:

For my dear wife, Emma.

Howard B. Wilson

For my loving wife, Evelyn, our departed cat, Patches, and my parents.

Louis H. Turcotte

Oqde`bd

to analyze various applications in mathematics and me-

chanics. The authors hope to encourage engineers and scientists to consider this

modern programming environment as an excellent alternative to languages such as

FORTRAN or C++. MATLAB 1 embodies an interactive environment with a high

level programming language supporting both numerical and graphical commands for

two- and three-dimensional data analysis and presentation. The wealth of intrinsic

mathematical commands to handle matrix algebra, Fourier series, differential equa-

tions, and complex-valued functions makes simple calculator operations of many

tasks previously requiring subroutine libraries with cumbersome argument lists.

We analyze problems, drawn from our teaching and research interests, empha-

sizing linear and nonlinear differential equation methods. Linear partial differential

equations and linear matrix differential equations are analyzed using eigenfunctions

and series solutions. Several types of physical problems are considered. Among

these are heat conduction, harmonic response of strings, membranes, beams, and

trusses, geometrical properties of areas and volumes, Ɲexure and buckling of inde-

terminate beams, elastostatic stress analysis, and multi-dimensional optimization.

Numerical integration of matrix differential equations is used in several examples

illustrating the utility of such methods as well as essential aspects of numerical ap-

proximation. Attention is restricted to the Runge-Kutta method which is adequate to

handle most situations. Space limitation led us to omit some interesting MATLAB

features concerning predictor-corrector methods, stiff systems, and event locations.

This book is not an introductory numerical analysis text. It is most useful as a ref-

erence or a supplementary text in computationally oriented courses emphasizing ap-

plications. The authors have previously solved many of the examples in FORTRAN.

Our MATLAB solutions consume over three hundred pages (over twelve thousand

lines). Although few books published recently present this much code, comparable

FORTRAN versions would probably be signifcantly longer. In fact, the conciseness

of MATLAB was a primary motivation for writing the book.

The programs contain many comments and are intended for study as separate en-

tities without an additional reference. Consequently, some deliberate redundancy

1 MATLAB is a registered trademark of The MathWorks, Inc. For additional information contact:

The MathWorks, Inc.

3 Apple Hill Drive

Natick, MA 01760-1500

(508) 647-7000, Fax: (508) 647-7001

Email: info@mathworks.com

This book uses MATLAB R

exists between program comments and text discussions. We also list programs in a

style we feel will be helpful to most readers. The source listings show line numbers

adjacent to the MATLAB code. MATLAB code does not use line numbers or permit

goto statements. We have numbered the lines to aid discussions of particular pro-

gram segments. To conserve space, we often place multiple MATLAB statements on

the same line when this does not interrupt the logical Ɲow.

All of the programs presented are designed to operate under the 6.x version of

MATLAB and Microsoft Windows. Both the text and graphics windows should be

simultaneously visible. A windowed environment is essential for using capabilities

like animation and interactive manipulation of three dimensional Ɯgures. The source

code for all of the programs in the book is available from the CRC Press website at

http://www.crcpress.com . The program collection is organized using an

independent subdirectory for each of the thirteen chapters.

This third edition incorporates much new material on time dependent solutions of

linear partial differential equations. Animation is used whenever seeing the solution

evolve in time is helpful. Animation illustrates quite well phenomena like wave

propagation in strings and membranes. The interactive zoom and rotation features in

MATLAB are also valuable tools for interpreting graphical output.

Most programs in the book are academic examples, but some problem solutions

are useful as stand-alone analysis tools. Examples include geometrical property cal-

culation, differentiation or integration of splines, Gauss integration of arbitrary order,

and frequency analysis of trusses and membranes.

A chapter on eigenvalue problems presents applications in stress analysis, elastic

stability, and linear system dynamics. A chapter on analytic functions shows the

efƜciency of MATLAB for applying complex valued functions and the Fast Fourier

Transform (FFT) to harmonic and biharmonic functions. Finally, the book concludes

with a chapter applying multidimensional search to several nonlinear programming

problems.

We emphasize that this book is primarily for those concerned with physical appli-

cations. A thorough grasp of Euclidean geometry, Newtonian mechanics, and some

mathematics beyond calculus is essential to understand most of the topics. Finally,

the authors enjoy interacting with students, teachers, and researchers applying ad-

vanced mathematics to real world problems.The availability of economical computer

hardware and the friendly software interface in MATLAB makes computing increas-

ingly attractive to the entire technical community. If we manage to cultivate interest

in MATLAB among engineers who only spend part of their time using computers,

our primary goal will have been achieved.

Howard B. Wilson

hwilson@bama.ua.edu

Louis H. Turcotte

turcotte@rose-hulman.edu

David Halpern

david.halpern@ua.edu

Advanced Math, Mechanics Applns using MATLAB 3rd ed. - H. Wilson, et al (CRC, 2003) WW.pdf

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