### Introduction

The main topic of this Section is the solution of PDEs using the method of separation of variables. In this method a PDE involving $n$ independent variables is converted into $n$ ordinary differential equations. (In this introductory account $n$ will always be 2.)

You should be aware that other analytical methods and also numerical methods are available for solving PDEs. However, the separation of variables technique does give some useful solutions to important PDEs.

#### Prerequisites

- be able to solve first and second order constant coefficient ordinary differential equations

#### Learning Outcomes

- apply the separation of variables method to obtain solutions of the heat conduction equation, the wave equation and the 2-D Laplace equation for specified boundary or initial conditions

#### Contents

1 Solution of important PDEs2 Method of separation of variables - general approach

2.1 Heat conduction equation

3 Method of separation of variables - specific solutions

4 Engineering Example 1

4.1 Heat conduction through a furnace wall