Ordinary Differential Equations with Applications

This book developed over 20 years of the author teaching the course at his own university. It serves as a text for a graduate level course in the theory of ordinary differential equations, written from a dynamical systems point of view. It contains both t

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34 Editors

J.E. Marsden L. Sirovich M. Golubitsky W. Jager Advisors

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

Springer New York Berlin Heidelberg Barcelona Hong Kong London Milan Paris Singapore Tokyo

Carmen Chicone

Ordinary Differential Equations with Applications

With 68 Illustrations

Springer

Carmen Chicone Department of Mathematics University of Missouri Columbia, MO 65211 USA [email protected] Series Editors J.E. Marsden Control and Dynamical Systems, 107-81 California Institute of Technology Pasadena, CA 91125 USA

L. Sirovich Division of Applied Mathematics Brown University Providence, RI 02912 USA

M. Golubitsky Department of Mathematics University of Houston Houston, TX 77204-3476 USA

W.Jager Department of Applied Mathematics Universitat Heidelberg Im Neuenheimer Feld 294 69120 Heidelberg Germany

Mathematics Subject Classification (1991): 34-01, 34A34, 34C35, 58Fxx Library of Congress Cataloging-in-Publication Data Chicone, Carmen Charles. Ordinary differential equations with applications/ Carmen Chicone. p. cm. — (Texts in applied mathematics; 34) Includes bibliographical references and index. ISBN 0-387-98535-2 (hardcover: alk. paper) 1. Differential equations. I. Title. II. Series. QA372.C5117 1999 515'.35-dc21 99-26376

© 1999 Springer-Verlag New York, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer-Verlag New York, Inc., 175 Fifth Avenue, New York, NY 10010, 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 herafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks and Merchandise Marks Act, may accordingly be used freely by anyone.

ISBN 0-387-98535-2 Springer-Verlag New York Berlin Heidelberg SPIN 10678928

To Jenny, for giving me the gift of time.

Preface

This book is based on a two-semester course in ordinary differential equations that I have taught to graduate students for two decades at the University of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of differential equations give away their point of view by the way they denote the derivative with respect to the independent variable, then the initiated reader can turn to Chapter 1, note that I write x, ˙ not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough introduction to the basic properties of differential equations that are needed

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