Introduction to partial differential equations

Introduction

What is a differential equation?

Equation that describes rates of change (derivatives) of a function of one or more variables

What is a partial differential equation (PDE)?

http://en.wikipedia.org/wiki/Partial_differential_equation - a type of differential equation involving an unknown function or functions of several independent variables and their partial derivatives with respect to those variables

http://mathworld.wolfram.com/PartialDifferentialEquation.html - an equation involving functions and their partial derivatives

Differential equations can either be solved analytically, i.e. for the general case, or they can be solved numerically

Analytical solutions of PDEs are difficult, and solution techniques often fail for non-trivial PDEs

Most of the time, modeling realistic problems requires numerical solution of PDEs

Ordinary differential equation (ODE) - function of one variable

Partial differential equation (PDE) - function of multiple variables