The divergence theorem is a theorem in vector calculus which relates the surface integral to the divergence inside the surface. Mathematically, it is stated as

\oiint{\scriptstyle S } \vec{F} \cdot \ \mathrm{d} \vec{s} = \iiint_D \nabla \cdot \vec{F} \,\mathrm{d}V

where D is the volume of the region enclosed by the surface and S is the projection of the surface onto the plane.

The divergence theorem holds in other dimensions as well; for example, for a flux integral in two dimensions, the divergence theorem becomes

\oint_S \vec{F} \cdot \vec{n} \ \mathrm{d} s = \iint_D \nabla \cdot \vec{F} \ \mathrm{d} A

which is a version of Green's theorem.

Ad blocker interference detected!

Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers

Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.