13.1 Separable Partial Differential Equations

13.2 Classical PDEs and Boundary-Value Problems

13.3 Heat Equation

13.4 Wave Equation

13.5 Laplace’s Equation

13.6 Nonhomogeneous Boundary-Value Problems

13.7 Orthogonal Series Expansions

13.8 Higher-Dimensional Problems

Chapter 13 in Review

In this and the next two chapters the emphasis will be on two procedures used in solving partial differential equations that occur in problems involving temperature distributions, vibrations, and potentials. These problems, called boundary-value problems (BVPs), are described by relatively simple linear second-order partial differential equations (PDEs). The thrust of these procedures is to find particular solutions of a linear PDE by reducing it to one or more linear ordinary differential equations.