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1. (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 ${\displaystyle \mathbf {n} }$, if a vector field ${\displaystyle \mathbf {F} }$ whose component functions have continuous first partial derivatives in W, then the flux of ${\displaystyle \mathbf {F} }$ through S is equal to the triple integral of the divergence of ${\displaystyle \mathbf {F} }$ over W, or ${\displaystyle \iint _{S}\mathbf {F} \cdot \mathbf {n} \,dS=\iiint _{W}\nabla \cdot \mathbf {F} \,dV}$.