Beginning Partial Differential Equations, 3rd Edition

Preface

This edition is based on four themes: methods of solution of initial-boundary value problems, properties and existence of solutions, applications of partial differential equations, and use of software to carry out computations and graphics.

The focus is on equations of diffusion processes and wave motion, and on Dirichlet and Neumann problems. Following an introductory chapter, we look at methods applied to these equations in bounded and unbounded media, and in one and several space dimensions. The topics are organized to make it easy to match problems in specific settings to methods for writing solutions. Methods include Fourier series and integrals, the use of characteristics, integral solutions, integral transforms, and special functions and eigenfunction expansions.

Properties of solutions that are considered include existence and uniqueness issues, maximum and mean value principles, integral representations, and sensitivity of solutions to initial and boundary conditions.

In addition to standard material for an introductory course, topics include traveling-wave solutions of Burger’s equation, damped wave motion, heat and wave equations with forcing terms, a general treatment of eigenfunction expansions, a complete solution of the telegraph equation using the Fourier transform, the use of characteristics to solve Cauchy problems and vibrating string problems with moving ends, double Fourier series solutions, and the Poisson-Kirchhoff integral solution of the wave equation ...