Partial Differential Equations 1

One Dimensional Heat Conduction Equation :

One Dimensional Wave Equation :

Elliptic Equation :

Hyperbolic Equation :

A solution y=y(t) of the equation a y'' + b y' +c y = 0can usually be found of the form _______________ for some constant k. : y = e

The three main types of PDEs : Parabolic, Elliptic and Hyperbolic

Solutions to Laplace's equation are called : harmonic functions

In some simple geometries, Laplace's equation can be solved by : separation of variables. Example: for a square, separate x and y.