tailieunhanh - Ebook Partial differential equations in action: Part 1

(BQ) Part 1 book "Partial differential equations in action" has contents: Introduction, diffusion, the laplace equation, scalar conservation laws and first order equations, waves and vibrations. | To Anna, my wife Sandro Salsa Partial Differential Equations in Action From Modelling to Theory Sandro Salsa Dipartimento di Matematica Politecnico di Milano CIP-Code: 2007938891 ISBN 978-88-470-0751-2 Springer Milan Berlin Heidelberg New York e-ISBN 978-88-470-0752-9 This work is subject to copyright. All rights are reserved, 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 other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the Italian Copyright Law in its current version, and permission for use must always ba obtained from Springer. Violations are liable to prosecution under the Italian Copyright Law. Springer is a part of Springer Science+Business Media c Springer-Verlag Italia, Milano 2008 Printed in Italy Cover-Design: Simona Colombo, Milan A Typesetting with L TEX: PTP-Berlin, Protago-TEX-Production GmbH, Germany () Printing and Binding: Grafiche Porpora, Segrate (MI) 9 8 7 6 5 4 3 2 1 Springer-Verlag Italia srl – Via Decembrio 28 – 20137 Milano-I 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 (PDE) during the last few years at the Politecnico of Milan. 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. The first one, chapters 2 to 5, has a rather elementary character with the goal of developing and .