divergence theorem

== English == === Proper noun === the divergence theorem (calculus) 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 n {\displaystyle \mathbf {n} } , if a vector field F {\displaystyle \mathbf {F} } whose component functions have continuous first partial derivatives in W, then the flux of F {\displaystyle \mathbf {F} } through S is equal to the triple integral of the divergence of F {\displaystyle \mathbf {F} } over W, or ∬ S F ⋅ n d S = ∭ W ∇ ⋅ F d V {\displaystyle \iint _{S}\mathbf {F} \cdot \mathbf {n} \,dS=\iiint _{W}\nabla \cdot \mathbf {F} \,dV} . ==== Related terms ==== fundamental theorem of calculus ==== Translations ==== === Further reading === divergence theorem on Wikipedia.Wikipedia