散度定理（Gauss定理）：穿过整个体积表面\(\partial V\)（闭曲面）的通量等于其体积微元散度之和，即
\[\oint_{\partial V} \vec{F} \cdot \vec{n} d S=\oint_V \operatorname{div} \vec{F} d V \]三维Gauss定理:
\[\iint_{\partial V} f_1 d y d z+f_2 d z d x+f_3 d x d y=\iiint_{V}\left(\frac{\partial f_1}{\partial x}+\frac{\partial f_2}{\partial y}+\frac{\partial f_3}{\partial z}\right) d x d y d z \]旋度定理：沿区域边界\(\partial S\)（闭曲线）的环量等于其区域面积微元旋度之和，即
\[ \oint_{\partial S^{+}} \vec{F} \cdot d\vec{L}=\oint_S \operatorname{rot} \vec{F} \cdot \vec{n}dS \]二维Green定理：
\[\int_{\partial S^{+}} f_{1} d x+f_{2} d y=\iint_S\left(\frac{\partial f_{2}}{\partial x}-\frac{\partial f_{1}}{\partial y}\right) d x d y \]三维Stokes定理：
\[ \int_{\partial S^{+}} f_{1}d x+f_{2} d y+f_{3} d z =\iint_{S}\left(\frac{\partial f_{3}}{\partial y}-\frac{\partial f_{2}}{\partial z}\right) d y d z+\left(\frac{\partial f_{1}}{\partial z}-\frac{\partial f_{3}}{\partial x}\right) d z d x+\left(\frac{\partial f_{2}}{\partial x}-\frac{\partial f_{1}}{\partial y}\right) d x d y \] 标签：right,frac,旋度,梯度,定理,散度,vec,partial,left From： https://www.cnblogs.com/BoyaYan/p/17237493.html