Mathematical Methods

12

Partial Differential Equations

12.1 Introduction

The reader is familiar with ordinary differential equations. These equations involve functions of a single variable only and their derivatives. In many problems that arise in geometry, physics, population dynamics, social sciences, medicine and engineering, one has to deal with equations containing functions of more than one variable and partial derivatives with respect to these independent variables. Such equations are called partial differential equations. Thus, a partial differential equation is an equation of the form

containing independent variables t, x, y, … an unknown function z