Partial Differential Equations in Action From Modelling to Theory
The book is intended as an advanced undergraduate or first-year graduate course for students from various disciplines, including applied mathematics, physics and engineering. It has evolved from courses offered on partial differential equations (PDEs) ove
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Sandro Salsa
Partial Differential Equations in Action From Modelling to Theory Third Edition
Sandro Salsa Dipartimento di Matematica Politecnico di Milano Milano, Italy
ISSN 2038-5722 UNITEXT – La Matematica per il 3+2 ISBN 978-3-319-31237-8 DOI 10.1007/978-3-319-31238-5
ISSN 2038-5757 (electronic) ISBN 978-3-319-31238-5 (eBook)
Library of Congress Control Number: 2016932390 © Springer International Publishing Switzerland 2016 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. Cover illustration: Simona Colombo, Giochi di Grafica, Milano, Italy Typesetting with LATEX: PTP-Berlin, Protago TEX-Production GmbH, Germany (www.ptp-berlin.de)
This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG Switzerland
To Anna, my wife
Preface
This book is designed as an advanced undergraduate or a first-year graduate course for students from various disciplines like applied mathematics, physics, engineering. It has evolved while teaching courses on partial differential equations (PDEs) during the last few years at the Politecnico di Milano. The main purpose of these courses was twofold: on the one hand, to train the students to appreciate the interplay between theory and modelling in problems arising in the applied sciences, and on the other hand to give them a solid theoretical background for numerical methods, such as finite elements. Accordingly, this textbook is divided into two parts, that we briefly describe below, writing in italics the relevant differences with the first edition, the second one being pretty similar. The first part, Chaps. 2 to 5, has a rather elementary character with the goal of developing and studying basic problems from the macro-areas of diffusion, propagation and transport, waves and vibrations. I have tried to emphasize, whenever possible, ideas and connections with concrete aspects, in order to provide intuition and feeling for
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