An Introduction to Partial Differential Equations

A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, paying particular emphasis to developing an appreciation of underlying mathematical theory. Beginning with basic definitions, properties and derivations of some basic equations of mathematical physics from basic principles, the book studies first order equations, classification of second order equations, and the one-dimensional wave equation. Two chapters are devoted to the separation of variables, whilst others concentrate on a wide range of topics including elliptic theory, Green's functions, variational and numerical methods. A rich collection of worked examples and exercises accompany the text, along with a large number of illustrations and graphs to provide insight into the numerical examples. Solutions to selected exercises are included for students whilst extended solution sets are available to lecturers from solutions@cambridge.org.

ISBN 052161323X   Pages 384 ISBN13 9780521613231 (What's this?)   Volumes 1 Publisher Cambridge University Press   Weight (grammes) 774 Imprint Cambridge University Press   Published in Cambridge Format Paperback   Previous ISBN 9780521848862 Publication date 12 May 2005   Height (mm) 247 Library of Congress 2005047096   Width (mm) 174 DEWEY 515.353   Spine width (mm) 18 DEWEY edition DC21   Academic level Tertiary education

1		Introduction		1
2		First-order equations		23
3		Second-order linear equations in two independent variables		64
4		The one-dimensional wave equation		76
5		The method of separation of variables		98
6		Sturm-Liouville problems and eigenfunction expansions		130
7		Elliptic equations		173
8		Green's functions and integral representations		208
9		Equations in high dimensions		226
10		Variational methods		282
11		Numerical methods		309
12		Solutions of odd-numbered problems		337

'Their book spans both introductory and advanced material, making it suitable for use right through a UK undergraduate degree. ... It stresses the practical applications of rigour, introduced with a touch sufficiently light not to put off the average student.' Times Higher Education Supplement 'The theoretical parts of the book are complemented by a good range of examples and problems. In summary, the book is a good introduction to the field that can be recommended for either class use or self-study.' Zeitschrift fur Angewandte Mathematik und Mechanik 'This is a thought-provoking book that links theory with applications and should be welcomed in any university library.' The Mathematical Gazette

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