Introduction

Abstract

Separation of variables is one of the most powerful methods for solving partial differential equations and one of the very few general methods that yield exact solutions. The idea is to seek for a solution which is a product (or a sum) of functions, each of which only depends on a single variable. The strength of this ansatz lies in reducing a partial differential equation in n variables to n differential equations in only one variable, since the theory of ordinary (single-variable) differential equations is far better developed than the theory of partial (multi-variable) differential equations.