Essentials of Mathematica_ With Applications to Mathematics and Physics [Boccara 2007-04-13].pdf

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Essentials of Mathematica
Nino Boccara
Essentials of Mathematica
With Applications to Mathematics and Physics
Springer
University of Illinois at Chicago
Department of Physics (M/C 273)
845 West Taylor Street
Chicago, IL 60607
USA
boccara@uic.edu
Library of Congress Control Number: 2006936428
ISBN-10: 0-387-49513-4
ISBN-13: 978-0-387-49513-2
Printed on acid-free paper.
© 2007 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the pubhsher (Springer Science-i-Business Media, LLC, 233 Spring Street, New York,
NY 10013, 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 in this publication of trade names, trademarks, service marks, and similar terms, even if
they 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.
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e-ISBN-10: 0-387-49514-2
e-ISBN-13: 978-0-387-49514-9
Preface
This book consists of two parts. Part I describes the essential
Mathematica
commands illustrated with many examples and Part II presents a variety of
applications to mathematics and physics showing how
Mathematica
could be
systematically used to teach these two disciplines.
The book is based on an introductory course taught at the University of
Illinois at Chicago to advanced undergraduate and graduate students of the
physics department who were not supposed to have any prior knowledge of
Mathematica.
Mathematica
is a huge mathematical software developed by Wolfram Research
Inc. It is an interactive high-level programming language that has all the
mathematics one is likely to need already built-in. Moreover, its interactivity
allows testing built-in and user-defined functions without difficulty thanks to
numerical, symbolic and graphic capabilities. All these features should en-
courage students to look at a problem in a computational way, and discover
the many benefits of this manner of thinking. For instance, when studying a
new problem,
Mathematica
makes it easy to test many examples that might
reveal unsuspected patterns.
The reader is advised to first study Chapter 1 of Part I entitled A Panorama
of
Mathematica
which presents an overview of the most frequently used com-
mands. The following chapters—dealing with Numbers, Algebra, Analysis,
Lists, Graphics, Statistics and Programming—go into more details. The reader
would probably make the most of the book browsing, as soon as possible, Part
II, devoted to Applications to Mathematics and Physics, coming back to Part
I to go deeper into specific commands and their various options.
This book is intended for beginners who want to be able to write a small
efficient
Mathematica
program in order to solve a given problem. Having this
in mind, we made every effort to follow the same technique: first the problem is
broken up into its different component parts, then each part of the problem is

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