Gauss divergence theorem

Published on: 20 February 2024


  1. Video Lecture

Divergence theorem / Gauss divergence theorem / Gauss’ theorem / Ostrogradsky’s theorem / Gauss-Ostrogradsky theorem

The divergence theorem relates an integral over a volume to an integral over the surface bounding that volume. The divergence theorem states that the integral of the divergence of a vector field over a volume is equal to the flux of that field through the surface bounding that volume.

$$ \int_{\mathcal V} \left( \nabla \cdot {\bf A} \right) dv = \oint_{\mathcal S} {\bf A}\cdot d{\bf s} $$