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Vector Calculus Formulas
Browse 0 reviewed vector calculus formulas with concrete inputs, outputs, calculations, applicability checks, and LaTeX.
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Vector Calculus
Divergence Theorem
\iiint_V \nabla\cdot\mathbf F\,dV=\iint_{\partial V}\mathbf F\cdot\mathbf n\,dSRelates volume divergence to outward flux across the boundary.
Open formulaVector Calculus
Green’s Theorem
\oint_C(P\,dx+Q\,dy)=\iint_D\left(\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)dARelates a planar line integral to a double integral over its enclosed region.
Open formulaVector Calculus
Stokes’ Theorem
\iint_S(\nabla\times\mathbf F)\cdot\mathbf n\,dS=\oint_{\partial S}\mathbf F\cdot d\mathbf rRelates surface curl to circulation around the oriented boundary.
Open formula