旋度

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向量微分算子 - 叉乘 -向量函数

\begin{aligned} C u r l (F) & = \nabla \times F = (\frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z}) \times (f_{1}, f_{2}, f_{3}) = | \begin{array}{c} i & j & k \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ f_{1} & f_{2} & f_{3} \end{array} | \end{aligned}

斯托克斯公式

$n$ 维广义旋度方程：

\begin{array}{r} \frac{\partial V_{i}}{\partial x_{i}} = \frac{\partial V_{j}}{\partial x_{j}} i, j = 1, 2, \dots, n \end{array}