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Michael Trott

The Mathematica GuideBook for Programming

With 315 Illustrations

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Springer

Michael Trott Wolfram Research Champaign, Illinois

Library of Congress Cataloging-in-Publication Data Trott, Michael. The mathematica guidebook : programming I Michael Trott. p. em. Includes bibliographical references and index. ISBN 0-387-94282-3 (alk. paper) I. Mathematica (Computer program language) I. Title. QA76.73.M29 T76 2000 510'.285'53042-dc21 00-030221

Additional material to this book can be downloaded from http://extras.springer.com ISBN 978-1-4612-6421-7 DOI 10.1007/978-1-4419-8503-3

ISBN 978-1-4419-8503-3 (eBook)

Printed on acid-free paper. © 2004 Springer Science+ Business Media New York Originally published by Springer Science+ Business Media, Inc. in 2004 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher Springer Science+Business Media, LLC 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 know or hereatler developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if the are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. (HAM) 9 8 7 6 5 4 3 2 springeronline.com

Preface Bei mathematischen Operationen kann so gar eine giinzliche Entlastung des Kopfes eintreten, indem man einmal ausgefohrte Ziihloperationen mit Zeichen symbolisiert und, statt die Hinifunktion auf Wiederholung schon ausgefohrter Operationen zu verschwenden, sie for wichtigere Fiille aufspart. When doing mathematics, instead of burdening the brain with the repetitive job of redoing numerical operations which have already been done before, it's possible to save that brainpower for more important situations by using symbols, instead, to represent those numerical calculations.

-Ernst Mach (1883) [45]

Computer Mathematics and Mathematica Computers were initially developed to expedite numerical calculations. A newer, and in the long run, very fruitful field is the manipulation of symbolic expressions. When these symbolic expressions represent mathematical entities, this field is generally called computer algebra [8]. Computer algebra begins with relatively elementary operations, such as addition and multiplication of symbolic expressions, and includes such things as factorization of integers and polynomials, exact linear algebra, solution of systems of equations, and logical operations. It also includes analysis operations, such as definite and indefinite integration, the solution of linear and nonlinear ordinary and partial differential equations, series expansions, and residue calculations. Today, with computer algebra systems, it is possible to calculate in minutes or hours the results that would (and did) take years to accomplish by