Curl

The amount that a vector field rotates around a point

$$\begin{array}{rl}\text{curl}\vec{F}& =\vec{\nabla }\times \vec{F}\\ & =\det \left(\begin{array}{ccc}{\hat{e}}_1& {\hat{e}}_2& {\hat{e}}_3\\ \frac{\partial }{\partial x}& \frac{\partial }{\partial y}& \frac{\partial }{\partial z}\\ F_1& F_2& F_3\end{array}\right)\\ & =⟨\frac{\partial F_3}{\partial y}-\frac{\partial F_2}{\partial z},\frac{\partial F_1}{\partial z}-\frac{\partial F_3}{\partial x},\frac{\partial F_2}{\partial x}-\frac{\partial F_1}{\partial y}⟩\end{array}$$