Math — Vector Calculus Theorems

\oint_C (P\,dx + Q\,dy) = \iint_R\!\left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right)dA

\oint_C \mathbf{F}\cdot d\mathbf{r} = \iint_S (\nabla\times\mathbf{F})\cdot d\mathbf{S}

\iiint_V (\nabla\cdot\mathbf{F})\,dV = \iint_{\partial V} \mathbf{F}\cdot d\mathbf{S}

\nabla\times(\nabla f) = \mathbf{0}