Introduction to Piecewise Differentiable Equations
This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of t
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Stefan Scholtes
Introduction to Piecewise Differentiable Equations
123
Stefan Scholtes Department of Engineering University of Cambridge Cambridge, UK
ISSN 2190-8354 ISSN 2191-575X (electronic) ISBN 978-1-4614-4339-1 ISBN 978-1-4614-4340-7 (eBook) DOI 10.1007/978-1-4614-4340-7 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012942479 Mathematics Subject Classification (2010): 90C26, 90C31, 90C33 and also 80M50, 34A34 © Stefan Scholtes 2012 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)
Introduction to Piecewise Differentiable Equations Stefan Scholtes
Preface
The aim of this manuscript is to provide an introduction to the theory of piecewise differentiable functions and, specifically, piecewise differentiable equations. The presentation is based on two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative
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