Computer Algebra Recipes For Mathematical Physics

This mathematical physics contribution to the Computer Algebra Recipes series is dedicated to my wife Karen, who lights my path through life. Richard H. Enns Computer Algebra Recipes for Mathematical Physics Birkh¨auser Boston • Basel • Berlin Richard H. Enns Simon Fraser University Department of Physics Burnaby, B.C. V5A 1S6 Canada AMS Subject Classifications (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 0-8176-3223-9 Printed on acid-free paper. c 2005 Birkh¨auser Boston All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Birkh¨auser Boston, c/o Springer Science+Business Media Inc., Rights and Permissions, 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. Printed in the United States of America. 987654321 www.birkhauser.com SPIN 10923559 (HP) Preface This book is a self-contained guide to problem-solving and exploration in mathematical physics using the powerful Maple 9.5 computer algebra system (CAS). With a CAS one cannot only crunch numbers and plot results, but also carry out the symbolic manipulations which form the backbone of mathematical physic