: Mathematics: divergence theorem

mathematical physics > vector calculus > divergence theorem

mathematical analysis > calculus > vector calculus > divergence theorem

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divergence theorem

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem which relates the flux of a vector field through a closed surface to the divergence of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that "the sum of all sources of the field in a region (with sinks regarded as negative sources) gives the net flux out of the region".
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Divergence_theorem)

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