Introduction

In this Section we continue to use the separation of variables method for solving PDEs but you will find that, to be able to fit certain boundary conditions, Fourier series methods have to be used leading to the final solution being in the (rather complicated) form of an infinite series. The techniques will be illustrated using the two-dimensional Laplace equation but similar situations often arise in connection with other important PDEs.

Prerequisites

• be familiar with the separation of variables method
• be familiar with trigonometric Fourier series

Learning Outcomes

• solve the 2-D Laplace equation for given boundary conditions and utilize Fourier series in the solution when necessary