divergence theorem

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English

Proper noun

divergence theorem

(calculus) A three-dimensional generalization of the fundamental theorem of calculus, which states that given a solid region W bounded by a closed surface S oriented by a unit normal vector $\mathbf {n}$ , if a vector field $\mathbf {F}$ whose component functions have continuous first partial derivatives in W, then the flux of $\mathbf {F}$ through S is equal to the triple integral of the divergence of $\mathbf {F}$ over W, or $\iint _{S}\mathbf {F} \cdot \mathbf {n} \,dS=\iiint _{W}\nabla \cdot \mathbf {F} \,dV$ .

Related terms

fundamental theorem of calculus

Translations

theorem

Asturian: teorema de la diverxencia m, teorema de Gauss m
Bulgarian: теорема на Гаус-Остроградски f (teorema na Gaus-Ostrogradski)
Catalan: teorema de la divergència m, teorema de Gauss m
French: théorème de flux-divergence m, théorème de Gauss m, théorème de la divergence m
Galician: teorema da diverxencia m
Italian: teorema della divergenza m, teorema di Gauss m
Portuguese: teorema da divergência m, teorema de Gauss m, teorema do divergente m
Spanish: teorema de la divergencia m, teorema de Gauss m

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