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Divergence Theorem

Statement

Let V be a region in space with boundary dV. Then the divergence theorem states that the volume integral of the divergence divergence F of F over V and the surface integral of F over the boundary dV of V are related by integral_V divergence F dV = integral_(dV)F·da.

Alternate names

Gauss-Ostrogradsky theorem | Gauss's theorem | Ostrogradsky's theorem

History

formulation date | 1762 (263 years ago)
formulator | Joseph-Louis Lagrange
status | proved
proof date | 1826 (64 years later) (199 years ago)
prover | Mikhail Vasilevich Ostrogradski
additional people involved | Carl Friedrich Gauss | George Green

Associated equation

integral_V divergence F dV = integral_(dV)F·da

Classes

solved mathematics problems | mathematics theorems

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