Series expansions and approximations
Chapter 12 dealt with infinite series of numbers and criteria for their convergence. In the same way one can study infinite series of functions $$\sum\limits_{k = 0}^\infty {{u_k}\left( x \right)} $$ where the functions uk (x) are all defined on a common
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Johannes-Kepler-University, Linz, Austria Edited by B. Buchberger and G. E. Collins
A. Ben-Israel
R. Gilbert Computer-Supported Calculus
Springer-Verlag Wien GmbH
Dr. Adi Ben-Israel Rutgers Center f orOperations Research and Department of Mathematics Rutgers University, New Brunswick, New Jersey, U.S.A.
Dr. Robert Gilbert Departmem of Mathematical Science and Computer and Infonnational Sciences University of Delaware, Newark, Delaware. U.S.A.
This work is subject 10 copyright. All fi ghts are reserved. whether the whole or part of the material is concerned, specifically those of translation, reprinti ng, re-use of illustrations, broadcasling, reproduction by photocopying machines or similar means, and storage in data banks. Product Liability: The publishcr can give no guarantee for allthe infannation contained in this book. This does also refer 10 in formation about drug dosage and application thereof. In every individual case the respective user must check its accuracy by consulting other phannaceutical literature. 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 protective laws and regulations and therefore free for general use. © 2002 Springer-Verlag Wien
O ri gin all y publ ishetl by Springer-\'erlag Wien Ne\\' Yor k in 2002 Sofleo\'er rt' pri nl of th e lI a rt!cm'er 1$1 etlition 2002
Data conversion by HD Ecker: TeXtservices, Bonn Printed onacid-feee and chlorine-free bleached paper
With 19 1 F ig ures
Libra ry ofCo ngress Cata loging-in-Publication Data Ben-Israel, Adi. Computer-supported calculus I A. Ben- Israel, R. Gilbert p. cm, - (Texts and monographs in symbolic computation, [SSN 0943-853X) Includes index. ISBN 978-3-7091-7230-8 ISBN 978-3-709 1-6 146-3 (eBook) DOI 10.1007/978-3-7091 -6146-3 I. Calculus-Data processing, 2, MACSYMA , I. Gilbert, Robert p" 1932- 11. Tille. lll. Series. QA303.5. D37B462oo1 515' .0285----dc21 200 1049370 ISSN 0943-853X ISBN 978-3-7091 -7230-8
Preface This is a new type of calculus book: Students who master this text will be well versed in calculus and, in addition, possess a useful working knowledge of one of the most important mathematical software systems, namely, MACSYMA. This will equip them with the mathematical competence they need for science and engineering and the competitive workplace. The choice of MACSYMA is not essential for the didactic goal of the book. In fact, any of the other major mathematical software systems, e.g., AXIOM, MATHEMATICA, MAPLE, DERIVE, or REDUCE, could have been taken for the examples and for acquiring the skill in using these systems for doing mathematics on computers. The symbolic and numerical calculations described in this book will be easily performed in any of these systems by slight modification of the syntax as soon as the student understands and masters the MACSYMA examples in this book. What is important, however, is that the student gets all the information necessary to design and execute the
