Partial Differential Equations: an Introduction

Intended for a college senior or first-year graduate-level course in partial differential equations, this text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Classical topics presented in a modern context include coverage of integral equations and basic scattering theory. This complete and accessible treatment includes a variety of examples of inverse problems arising from improperly posed applications. Exercises at the ends of chapters, many with answers, offer a clear progression in developing an understanding of this essential area of mathematics. 1988 edition.

Title Page; Copyright Page; Preface; ACKNOWLEDGMENTS; Table of Contents; Chapter 1 -- Introduction; 1.1 PHYSICAL EXAMPLES; 1.2 FIRST ORDER LINEAR EQUATIONS; 1.3 CLASSIFICATION OF SECOND ORDER EQUATIONS AND CANONICAL FORMS; 1.4 FOURIER SERIES AND INTEGRALS; * 1.5 ANALYTIC FUNCTIONS; 1.6 A BRIEF HISTORY OF THE THEORY OF PARTIAL DIFFERENTIAL EQUATIONS; Chapter 2 -- The Wave Equation; 2.1 THE WAVE EQUATION IN TWO INDEPENDENT VARIABLES; 2.2 THE CAUCHY PROBLEM FOR HYPERBOLIC EQUATIONS IN TWO INDEPENDENT VARIABLES; 2.3 THE CAUCHY PROBLEM FOR THE WAVE EQUATION IN MORE THAN TWO INDEPENDENT VARIABLES.

2.4 THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE WAVE EQUATION IN TWO INDEPENDENT VARIABLES2.5 FOURIER'S METHOD FOR THE WAVE EQUATION IN THREE INDEPENDENT VARIABLES; 2.6 THE EQUATIONS OF GAS DYNAMICS; Chapter 3 -- The Heat Equation; 3.1 THE WEAK MAXIMUM PRINCIPLE FOR PARABOLIC EQUATIONS; 3.2 THE INITIAL-BOUNDARY VALUE PROBLEM FOR THE HEAT EQUATION IN A RECTANGLE; 3.3 CAUCHY'S PROBLEM FOR THE HEAT EQUATION; 3.4 REGULARITY OF SOLUTIONS TO THE HEAT EQUATION; * 3.5 THE STRONG MAXIMUM PRINCIPLE FOR THE HEAT EQUATION; * 3.6 THE STEFAN PROBLEM AND ANALYTIC CONTINUATION.

3.7 HERMITE POLYNOMIALS AND TH…