A partial differential equation is an equation that involves derivatives with respect to more than one variable. Many of the equations used to model the physics of the real world are partial differential equations. Maxwell's equations are a famous example.

 

Another example involving waves concerns a wave in two dimensions with an amplitude (height) U which depends on time t and also on the two distance measurements x and y along mutually perpendicular axes. The differential equation representing the wave is

 

    δU ²δx ² + δU ²δy ² = 1/c² δU ²δt ²

 

where c is the wave's velocity. When solved, the solution U will give the amplitude of the wave at any point (x, y).

 

Symbols such as δx ² are called partial derivatives.