Functional Analysis in Mechanics
This book offers a brief, practically complete, and relatively simple introduction to functional analysis. It also illustrates the application of functional analytic methods to the science of continuum mechanics. Abstract but powerful mathematical notions
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Leonid P. Lebedev • Iosif I. Vorovich Michael J. Cloud
Functional Analysis in Mechanics Second Edition
Leonid P. Lebedev Department of Mathematics National University of Colombia Bogotá, Colombia
Iosif I. Vorovich † Department of Mathematics & Mechanics Rostov State University Rostov-on-Don, Russia
Michael J. Cloud Department of Electrical Engineering Lawrence Technological University Southfield, MI, USA
ISSN 1439-7382 ISBN 978-1-4614-5867-8 ISBN 978-1-4614-5868-5 (eBook) DOI 10.1007/978-1-4614-5868-5 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012950048 Mathematics Subject Classification (2010): 4601, 4602, 7401, 7402, 74B05, 74K25, 35JXX, 35A01, 35A02 © Springer Science+Business Media, LLC 2003, 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
In Russia, a university Mechanics department will typically exist within a “Mathematical Faculty.” Such a department is not an engineering department in the western sense, but is something intermediate between a mathematics department and an engineering department. It will offer courses on calculus, linear algebra, analysis, differential geometry, differential equations, and so on, along with extensive courses
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