## Quick Reference

A theorem that gives the relation between the total flux of a vector *F* out of a surface *S*, which surrounds the volume *V*, to the vector inside the volume. The divergence theorem states that *∫*_{v}div FdV = *∫**F*·dS. The divergence theorem is also known as **Gauss' theorem** and **Ostrogradsky's theorem** (named after the Russian mathematician Michel Ostrogradsky (1801–61), who stated it in 1831). Gauss' law for electric fields is a particular case of the divergence theorem.

*∫*_{v}div FdV = *∫**F*·dS.

*Subjects:*
Physics.

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