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20

Editors Stuart Antman Philip Holmes K.R. Sreenivasan

Advisors G. Iooss P. Holmes D. Barkley M. Dellnitz P. Newton

For further volumes: http://www.springer.com/series/1214

Mark H. Holmes

Introduction to Perturbation Methods Second Edition

123

Mark H. Holmes Department of Mathematical Sciences Rensselaer Polytechnic Institute 110 8th Street Troy, NY 12180-3590

ISSN 0939-2475 ISBN 978-1-4614-5476-2 ISBN 978-1-4614-5477-9 (eBook) DOI 10.1007/978-1-4614-5477-9 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012951042 Mathematics Subject Classification (2010): 34-XX , 34D15, 34Exx, 35-XX, 35B25, 35B27, 76-XX, 76M45, 41-XX, 41A60 © Springer Science+Business Media New York 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

To Colette, Matthew, and Marianna A small family with big hearts

Preface

First, let me say hello and welcome to the subject of perturbation methods. For those who may be unfamiliar with the topic, the title can be confusing. The first time I became aware of this was during a family reunion when someone asked what I did as a mathematician. This is not an easy question to answer, but I started by describing how a certain segment of the applied mathematics community was interested in problems that arise f