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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 (262 years ago) formulator | Joseph-Louis Lagrange status | proved proof date | 1826 (64 years later) (198 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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