Divergence Theorem

The divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that the sum of all sources minus the sum of all sinks gives the net flow out of a region. $$ \iiint_V ( \nabla \cdot \mathbf{F} ) dV = \oint \oint_S ( \mathbf{F} \cdot \mathbf{n} ) dS $$