Green's function

The fundamental solution encoding how a point source's effect spreads out -- superpose it to solve for any source distribution.

A Green's function $G$ is the fundamental solution of a linear differential operator sourced by a single point (a Dirac delta). Once known, the solution for ANY source distribution follows by superposition -- integrating $G$ against that distribution.

Examples

In 3D, the free-space Green's function for the Laplacian is $G(\mathbf{r})=-1/(4\pi|\mathbf{r}|)$ , the familiar $1/r$ potential.