# Dictionary:Green's theorem

A form of Gauss's (divergence) theorem relating a volume integral to surface integrals.

If *F* and *G* are two scalar functions, then

where *dv* is a volume element and is a directed surface element, represented by .
Here is the inward directed normal vector to the surface.

Named for George Green (1793-1841), English mathematician.

## Derivation and applications

See derivation and application.