ABSTRACT

Separation of variables is one of the oldest and most efficient solution techniques for a certain class of partial differential equations problems. This chapter shows the application of separation of variables to initial boundary value problems for the heat and wave equations, and to boundary value problems for the Laplace equation. Generally speaking, the method of separation of variables is applied to initial boundary value problems for the wave equation in much the same way as for the heat equation. The chapter considers the two-dimensional analog of the wave equation and solves it by the method of separation of variables in terms of both Cartesian and polar coordinates.