# Gauss theorem

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Also known as **divergence theorem**. For a scalar field :

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

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Also known as **divergence theorem**. For a scalar field $A$:

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

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