Editing Partial differential equation (section)

===Integral transform===
An [[integral transform]] may transform the PDE to a simpler one, in particular, a separable PDE. This corresponds to diagonalizing an operator.

An important example of this is [[Fourier analysis]], which diagonalizes the heat equation using the [[eigenbasis]] of sinusoidal waves.

If the domain is finite or periodic, an infinite sum of solutions such as a [[Fourier series]] is appropriate, but an integral of solutions such as a [[Fourier integral]] is generally required for infinite domains. The solution for a point source for the heat equation given above is an example of the use of a Fourier integral.