Methods of Mathematical Modelling Continuous Systems and Differentia
This book presents mathematical modelling and the integrated process of formulating sets of equations to describe real-world problems. It describes methods for obtaining solutions of challenging differential equations stemming from problems in areas such
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Thomas Witelski Mark Bowen
Methods of Mathematical Modelling Continuous Systems and Differential Equations
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
Thomas Witelski Mark Bowen •
Methods of Mathematical Modelling Continuous Systems and Differential Equations
123
Thomas Witelski Department of Mathematics Duke University Durham, NC USA
Mark Bowen International Center for Science and Engineering Programs Waseda University Tokyo Japan
ISSN 1615-2085 ISSN 2197-4144 (electronic) Springer Undergraduate Mathematics Series ISBN 978-3-319-23041-2 ISBN 978-3-319-23042-9 (eBook) DOI 10.1007/978-3-319-23042-9 Library of Congress Control Number: 2015948859 Mathematics Subject Classification: 34-01, 35-01, 34Exx, 34B40, 35Qxx, 49-01, 92-XX 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)
For Yuka and Emma, For Mom and Hae-Young, and For students seeking mathematical tools to model new challenges…
Preface
What is Mathematical Modelling? In order to explain the purpose of modelling, it is helpful to start by asking: what is a mathematical model? One answer was given by Rutherford Aris [4]: A model is a set of mathematical equations that … provide an adequate description of a physical system.
Dissecting the words in his description, “a physical system” can be broadly interpreted as any real-world problem
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