旋度

Curl 向量微分算子 - 叉乘 -向量函数

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}$$