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[...]... Bibliography 375 Index 379 Computer Algebra Recipes for Mathematical Physics INTRODUCTION The purpose of computing is insight, not numbers R.W Hamming, Numerical Methods for Scientists and Engineers (1973) Science means simply the aggregate of all the recipes that are always successful Paul Val´ry, French poet and essayist (1871–1945) e A Computer Algebra Systems Computer algebra systems (CASs) are... modifying the recipes to his or her own taste This is because the Maple input and output is completely annotated for each recipe and the underlying mathematics and physics fully explained 2 INTRODUCTION B Computer Algebra Recipes The heart of this text consists of a systematic collection of computer algebra recipes which have been designed to illustrate the concepts and methods of mathematical physics and... Chapter 1 Supplementary recipes can be used in two different ways They can be regarded as problems to be solved by using the mathematical physics concepts and computer algebra techniques presented in the main text recipes Your solutions can then be compared with those that I have presented Even if you are successful, you probably will be interested in the many little computer algebra features that are... additional recipes can be regarded as still more interesting applications of computer algebra to mathematical physics Enjoy exploring all the recipes! MAPLE HELP 3 C Maple Help In this text, the Maple commands are introduced on a need-to-know basis If you wish to learn more about these commands, or about other possible commands which might prove useful in solving a particular mathematical physics problem,... guide to what is possible in mathematical physics using a CAS, the possibilities being limited only by your own background and desires At the end of each chapter, Supplementary Recipes are presented in the form of problems, their fully annotated solutions (recipes) being included on the CD These recipes are also hyperlinked to the recipe index file with a simple numbering system For example, 01-S02 is the... Butler described a fictitious land in the utopian novel Erewhon, the title being intended as an anagram for nowhere In this land, the people dealt with disease as a crime and destroyed machinery lest machines destroyed them This would not be the land for using computer algebra, so in the Computer Algebra Recipes series, I have introduced a fictitious planet, Erehwon, where names are occasionally spelled... languages and to plot the results in a wide variety of ways, but to also perform lengthy and complicated symbolic mathematical manipulations as well The purpose of this text is to show how a CAS can be used to tackle problem-solving and exploration of concepts and methods in mathematical physics A CAS can perform a wide variety of mathematical operations, including • analytic differentiation and analytic/numerical... important mathematical physics example and, where feasible, the example is presented in a “story” format wherein real or fictitious characters motivate or explain the recipe Every topic or story in the text contains the Maple code or recipe to explore that particular topic To make life easier for you, all recipes have been placed on the CD-ROM enclosed within the back cover of this text The recipes are... So the general solution of the homogeneous ODE is of the form C1 eλ1 x + C2 eλ2 x , the specific forms of λ1 and λ2 being easily identified from the above Maple output The variation of parameters method then assumes that y(x) = C1(x) eλ1 x + C2(x) eλ2 x for the complete LODE, and solves for the functions C1(x) and C2(x) See, for example, [Ste87] for the details The infolevel[dsolve] command can be turned... (lhs) of the operator and the time-dependent form of Y on the right-hand side (rhs) Assigned quantities can be mathematically manipulated The symbols *, /, +, -, and ˆ are used for multiplication, division, addition, subtraction, and exponentiation, The Maple forms cos and exp of the cosine and exponential commands are intuitively obvious Y := INTRODUCTORY RECIPES 5 Differentiating Y once with respect . (2000): 15A90, 30-XX, 33-XX, 34-XX, 35-XX, 35Qxx, 40-XX, 42-XX, 44-XX, 49-XX, 65-XX, 68-XX, 70-XX, 97U50 ISBN 0-8 17 6-3 22 3-9 Printed on acid-free paper. c 2005. Enns Computer Algebra Recipes for Mathematical Physics Birkh ¨ auser Boston • Basel • Berlin Richard H. Enns Simon Fraser University Department of Physics Burnaby,