divergence theorem

Meanings

1. A three-dimensional generalization of the fundamental theorem of calculus, which states that given a solid region W bounded by a closed surface S oriented by a unit normal vector mathbf n, if a vector field mathbf F whose component functions have continuous first partial derivatives in W, then the flux of mathbf F through S is equal to the triple integral of the divergence of mathbf F over W, or ∬_S mathbf F· mathbf n,dS=∭_W∇· mathbf F,dV.