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All there is to know about functional analysis, integral equations and calculus of variations in one handy volume, written for the specific needs of physicists and applied mathematicians.The new edition of this handbook starts with a short introduction to functional analysis, including a review of complex analysis, before continuing a systematic discussion of different types of integral equations. After a few remarks on the historical development, the second part provides an introduction to the calculus of variations and the relationship between integral equations and applications of the calculus of variations. It further covers applications of the calculus of variations developed in the second half of the 20th century in the fields of quantum mechanics, quantum statistical mechanics and quantum field theory.Throughout the book, the author presents a wealth of problems and examples often with a physical background. He provides outlines of the solutions for each problem, while detailed solutions are also given, supplementing the materials discussed in the main text. The problems can be solved by directly applying the method illustrated in the main text, and difficult problems are accompanied by a citation of the original references.Highly recommended as a textbook for senior undergraduates and first-year graduates in science and engineering, this is equally useful as a reference or self-study guide.
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Michio Masujima Applied Mathematical Methods in Theoretical Physics Related Titles Vaughn, M. T. Introduction to Mathematical Physics 2007 ISBN: 978-3-527-40627-2 Trigg, G. L. (ed.) Mathematical Tools for Physicists 2005 ISBN: 978-3-527-40548-0 Boas, M. L. Mathematical Methods in the Physical Sciences International Edition 2005 ISBN: 978-0-471-36580-8 Tinker, M., Lambourne, R. Further Mathematics for the Physical Sciences 2000 ISBN: 978-0-471-86691-6 Michio Masujima Applied Mathematical Methods in Theoretical Physics Second, Enlarged and Improved Edition The Author Dr. Michio Masujima Tokyo, Japan All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by the Deutsche Nationalbibliothek Die Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.d-nb.de. 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form – by photoprinting, microfilm, or any other means – nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Composition Laserwords Private Limited, Chennai, India Printing Strauss GmbH, M¨orlenbach Bookbinding Litges & Dopf GmbH, Heppenheim Cover Design K. Schmidt Printed in the Federal Republic of Germany Printed on acid-free paper ISBN: 978-3-527-40936-5 To my granddaughter, Honoka VII Contents Preface XI Introduction XV 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 Function Spaces, Linear Operators, and Green’s Functions Function Spaces 1 Orthonorma