An Introduction to Partial Differential Equations

Yehuda Pinchover, Jacob Rubinstein

• Publisher: Cambridge University Press
• Year: 2005
• Print ISBN: 9780521613231
• eBook ISBN: 9780511110252
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

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 [email protected].

Table of contents

• Cover
• Title Page
• Copyright
• Contents
• Preface
• 1 Introduction
• 2 First-order equations
• 3 Second-order linear equations in two independent variables
• 4 The one-dimensional wave equation
• 5 The method of separation of variables
• 6 Sturm–Liouville problems and eigenfunction expansion
• 7 Elliptic equations
• 8 Green’s functions and integral representations
• 9 Equations in high dimensions
• 10 Variational methods
• 11 Numerical methods
• 12 Solutions of odd-numbered problems
• References
• Index