Overview
Gauss' theorem applies to a differential vector field (typically defined on {% \mathbb{R}^3 %}) and relates the amount of flow (suitably defined) through a closed surface, to the integral of the divergence of the vector field on the interior of the surface.
Statement
{% \int \int \vec{F} \cdot d\vec{A} = \int \int \int \nabla \cdot \vec{F} dV %}