Gauss theorem

Also known as divergence theorem. For a scalar field Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} :

$\int _{\partial \Omega }A\cdot d{\vec {S}}=\int _{\Omega }\nabla AdV.$

It trivialy generalizes to vector fields, by applying it to each Cartesian component.