Integral Theorems

Abstract

If F is a vector-valued function with continuous partial derivatives throughout a region V, and V is surrounded by a closed surface S, then

$$\int_V {\nabla \cdot FdV = } \int_S {F \cdot dS} $$

This result is known as Gauss’s Flux Theorem or Gauss’s Divergence Theorem (or sometimes just as the Divergence Theorem).