斯托克斯公式

Stokes' theorem
格林公式的推广
借助行列式记忆

\begin{aligned} \oint_{Γ} P d x + Q d y + R d z \\ = \iint_{Σ} (\frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z}) d y d z + (\frac{\partial P}{\partial z} - \frac{\partial R}{\partial x}) d z d x + (\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}) d x d y \\ = \iint_{Σ} | \begin{array}{c} \cos α & \cos β & \cos γ \\ \frac{\partial}{\partial x} & \frac{\partial}{\partial y} & \frac{\partial}{\partial z} \\ P & Q & R \end{array} | \end{aligned}