This book is an introduction to partial differential equations for students who have finished calculus through ordinary differential equation. It provides physical motivation, mathematical method, and physical application.
Each section of the book contains numerous worked examples and set of exercises. These exercises have been kept to a uniform level of difficulty, and solutions to nearly 450 to 700 exercises in the text have been provided. Chapter 0 is a brief introduction to the entire subject of partial equations and some technical material that is used frequently throughout the book. Chapter 1 to 4 contains the basic material on Fourier series and boundary-value problems in rectangular, cylindrical, and spherical coordinates. Chapter 5 develops Fourier transform and applies them to solve problems in unbounded regions. Chapter 6 to 8 is an asymptotic analysis, numerical analysis, and Green’s functions for instructors who may have additional time or wish to omit some of the earlier material.