斯托克斯公式

Stokes’ theorem 格林公式的推广 借助行列式记忆

&\oint_{\Gamma} P\mathrm{d}x+Q\mathrm{d}y+R\mathrm{d}z \\ &=\iint \limits_{\Sigma} (\dfrac{\partial R}{\partial y}-\dfrac{\partial Q}{\partial z})\mathrm{d}y\mathrm{d}z+(\dfrac{\partial P}{\partial z}-\dfrac{\partial R}{\partial x} )\mathrm{d}z\mathrm{d}x+(\dfrac{\partial Q}{\partial x}-\dfrac{\partial P}{\partial y} )\mathrm{d}x\mathrm{d}y \\ &=\iint \limits_{\Sigma} \begin{vmatrix} \cos \alpha & \cos \beta & \cos\gamma \\ \dfrac{\partial }{\partial x} & \dfrac{\partial }{\partial y} & \dfrac{\partial }{\partial z} \\ P & Q & R \end{vmatrix} \end{align}$$ [[旋度\|旋度]]