Curl(\mathbf{F})&=\nabla \times \mathbf{F} =(\dfrac{\partial }{\partial x},\dfrac{\partial }{\partial y},\dfrac{\partial }{\partial z} )\times(f_{1},f_{2},f_{3}) =
\begin{vmatrix}
i & j & k \\
\dfrac{\partial }{\partial x} & \dfrac{\partial }{\partial y} & \dfrac{\partial }{\partial z} \\
f_{1} & f_{2} & f_{3}
\end{vmatrix}
\end{align}$$
[[斯托克斯公式\|斯托克斯公式]]
$n$ 维广义旋度方程:
$$\begin{align}
\dfrac{\partial V_{i}}{\partial x_{i}} =\dfrac{\partial V_{j}}{\partial x_{j}}\quad i,j=1,2,\cdots,n
\end{align}$$