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 ∫vdiv 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.
∫vdiv FdV = ∫F·dS.