Fourier series and boundary value problems.

摘要

Boundary value problems consist of either an ordinary differential equation or a partial differential equation, which describes a phenomena in space and time. They also include boundary conditions, which are based on the dimensions or describe the initial state of the object. In studying boundary value problems, we are seeking a function that satisfies the ordinary or partial differential equation and the given boundary conditions. We will be looking at boundary value problems with second-order linear partial differential equations. The primary method for solving such problems is separation of variables which reduces the one boundary value problem with the partial differential equation to several each with an ordinary differential equation. In trying to satisfy the nonhomogeneous boundary conditions, we use Fourier series theory.