Essential Partial Differential Equations Analytical and Computationa
This volume provides an introduction to the analytical and numerical aspects of partial differential equations (PDEs). It unifies an analytical and computational approach for these; the qualitative behaviour of solutions being established using classical
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David F. Griffiths John W. Dold David J. Silvester
Essential Partial Differential Equations Analytical and Computational Aspects
Springer Undergraduate Mathematics Series Advisory Board M.A.J. Chaplain, University of Dundee, Dundee, Scotland, UK K. Erdmann, University of Oxford, Oxford, England, UK A. MacIntyre, Queen Mary University of London, London, England, UK E. Süli, University of Oxford, Oxford, England, UK M.R. Tehranchi, University of Cambridge, Cambridge, England, UK J.F. Toland, University of Cambridge, Cambridge, England, UK
More information about this series at http://www.springer.com/series/3423
David F. Griffiths John W. Dold David J. Silvester •
Essential Partial Differential Equations Analytical and Computational Aspects
123
David F. Griffiths University of Dundee Fife UK
David J. Silvester School of Mathematics The University of Manchester Manchester UK
John W. Dold School of Mathematics The University of Manchester Manchester UK
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-319-22568-5 ISBN 978-3-319-22569-2 (eBook) DOI 10.1007/978-3-319-22569-2 Library of Congress Control Number: 2015948777 Mathematics Subject Classification (2010): 35-01, 65L10, 65L12, 65L20, 65M06, 65M12, 65N06, 65N12 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 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 Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
In mathematics you don’t understand things. You just get used to them. John von Neumann “Begin at the beginning”, the King said, very gravely, “and go on till you come to the end: then stop”. Lewis Carroll, Alice in Wonderland
Preface
This textbook is a self-contained introduction to the mathematical aspects of partial differential equations. The book is aimed at undergraduate students studying for a mathematics degree. Select
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