Composite Asymptotic Expansions: General Study
In this chapter, we present the general theory of ca se s: their definition and their behavior with respect to the basic operations of addition, multiplication, division, differentiation, integration, composition and analytic continuation. We also link ou
- PDF / 2,523,079 Bytes
- 169 Pages / 439.36 x 666.15 pts Page_size
- 65 Downloads / 237 Views
For further volumes: http://www.springer.com/series/304
2066
•
Augustin Fruchard
Reinhard Sch¨afke
Composite Asymptotic Expansions
123
Augustin Fruchard Laboratoire de Math´ematiques, Informatique et Applications Universit´e de Haute Alsace Mulhouse France
Reinhard Sch¨afke Institut de Recherche Math´ematique Avanc´ee Universit´e de Strasbourg Strasbourg France
ISBN 978-3-642-34034-5 ISBN 978-3-642-34035-2 (eBook) DOI 10.1007/978-3-642-34035-2 Springer Heidelberg New York Dordrecht London Lecture Notes in Mathematics ISSN print edition: 0075-8434 ISSN electronic edition: 1617-9692 Library of Congress Control Number: 2012953999 Mathematics Subject Classification (2010): 41A60, 34E, 34M30, 34M60 c Springer-Verlag Berlin Heidelberg 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)
Preface
The purpose of this memoir is to present a theory of asymptotic expansions for functions of two variables, using at the same time functions of one variable and functions of the quotient of these two variables. These composite asymptotic expansions (CAsEs for short) are particularly well suited to the description of solutions of singularly perturbed ordinary differential equations. Their use is classical for boundary layers, but less familiar near turning points.
Data Loading...
