Divergence Theorem

Divergence Theorem:

$\oiint_{\partial\Omega} \vec{F} \cdot d\vec{A} = \iiint_{\Omega} (\nabla \cdot \vec{F}) dV$

In Vector Calculus, the Divergence Theorem gives equivalence between a closed surface and the volume it bounds.

Given a vector function $\vec{F}(x,y,z)$ , and a 3D region $\Omega$ (with $\partial\Omega$ representing the boundary of $\Omega$ ),

The integral of $\vec{F}$ over $\partial\Omega$ is equal to the integral of the divergence of $\vec{F} (\nabla \cdot \vec{F})$ over $\Omega$ .