Ordinary Differential Equations: Basics and Beyond
This book develops the theory of ordinary differential equations (ODEs), starting from an introductory level (with no prior experience in ODEs assumed) through to a graduate-level treatment of the qualitative theory, including bifurcation theory (but not
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David G. Schaeffer John W. Cain
Ordinary Differential Equations: Basics and Beyond
Texts in Applied Mathematics Volume 65
Editors-in-chief: S.S. Antman, University of Maryland, College Park, USA L. Greengard, New York University, New York City, USA P.J. Holmes, Princeton University, Princeton, USA
Series Editors: J. Bell, Lawrence Berkeley National Lab, Berkeley, USA J. Keller, Stanford University, Stanford, USA R. Kohn, New York University, New York City, USA P. Newton, University of Southern California, Los Angeles, USA C. Peskin, New York University, New York City, USA R. Pego, Carnegie Mellon University, Pittburgh, USA L. Ryzhik, Stanford University, Stanford, USA A. Singer, Princeton University, Princeton, USA A. Stevens, Universit¨at M¨unster, M¨unster, Germany A. Stuart, University of Warwick, Coventry, UK T. Witelski, Duke University, Durham, USA S. Wright, University of Wisconsin-Madison, Madison, USA
More information about this series at http://www.springer.com/series/1214
David G. Schaeffer • John W. Cain
Ordinary Differential Equations: Basics and Beyond
123
David G. Schaeffer James B. Duke Professor of Mathematics, Emeritus Department of Mathematics Duke University Durham, NC, USA
John W. Cain Mathematics Department Harvard University Cambridge, MA, USA
ISSN 0939-2475 ISSN 2196-9949 (electronic) Texts in Applied Mathematics ISBN 978-1-4939-6387-4 ISBN 978-1-4939-6389-8 (eBook) DOI 10.1007/978-1-4939-6389-8 Library of Congress Control Number: 2016945045 Mathematics Subject Classification (2010): 34-01, 37-01, 00-01 © Springer Science+Business Media New York 2016 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer Science+Business Media LLC The registered company address is 233 Spring Street, New York, NY 10013, U.S.A
Figure 1: Being literal about the phrase “bathtub model”: A whimsical representation of the positive feedback in Sel’kov’s
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