Ordinary and Partial Differential Equations With Special Functions,
This textbook provides a genuine treatment of ordinary and partial differential equations (ODEs and PDEs) through 50 class tested lectures. Key Features: Explains mathematical concepts with clarity and rigor, using fully worked-out examples and helpf
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Ravi P. Agarwal Donal O’Regan
Ordinary and Partial Differential Equations With Special Functions, Fourier Series, and Boundary Value Problems
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Ravi P. Agarwal Florida Institute of Technology Department of Mathematical Sciences 150 West University Blvd. Melbourne, FL 32901 [email protected]
ISBN: 978-0-387-79145-6 DOI 10.1007/978-0-387-79146-3
Donal O’Regan National University of Ireland, Galway Mathematics Department University Road Galway, Ireland [email protected]
e-ISBN: 978-0-387-79146-3
Library of Congress Control Number: 2008938952 Mathematics Subject Classification (2000): 00-01, 34-XX, 35-XX c Springer Science+Business Media, LLC 2009 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, 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 on acid-free paper springer.com
Dedicated to our Sons Hans Agarwal and Daniel Joseph O’Regan
Preface This book comprises 50 class-tested lectures which both the authors have given to engineering and mathematics major students under the titles Boundary Value Problems and Methods of Mathematical Physics at various institutions all over the globe over a period of almost 35 years. The main topics covered in these lectures are power series solutions, special functions, boundary value problems for ordinary differential equations, Sturm– Liouville problems, regular and singular perturbation techniques, Fourier series expansion, partial differential equations, Fourier series solutions to initial-boundary value problems, and Fourier and Laplace transform techniques. The prerequisite for this book is calculus, so it can be used for a senior undergraduate course. It should also be suitable for a beginning graduate course because, in undergraduate courses, students do not have any exposure to various intricate concepts, perhaps due to an inadequate level of mathematical sophistication. The content in a particular lecture, together with the problems therein, provides fairly adequate coverage of the topic under study. These lectures have been delivered in one year courses and provide flexibility in the choice of material for a particular one-semester course. Throughout this book, the mathematical concepts have been explained very carefully in the simplest possible terms, and illustrated by a number of complete workout examples. Like any other mathematical book, it does contain som
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