Gauss theorem
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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} :
- 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 \int_{\partial\Omega} A \cdot d\vec{S} = \int_\Omega \nabla A dV .}
It trivialy generalizes to vector fields, by applying it to each Cartesian component.