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\index{d@定理!s@Stokes formula}
Let $\Gamma$ be a piecewise smooth directed closed curve, $\Sigma$ is a piecewise smooth directed surface bounded by $\Gamma$, the side of $\Gamma$ and the positive direction of $\Sigma$ According to the right-hand rule, if the function $P(x,y,z)$, $Q(x,y,z)$, $R(x,y,z)$ has a first-order continuous deviation on the curve $\Sigma$ Derivative, then
\begin{multline}
- \iint_\Sigma\left(\frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z}\right)\mathrm{d}y\mathrm{d}z + \left(\frac{\partial P}{\partial z} - \frac{\partial R}{\partial x}\right)\mathrm{d}z\mathrm{d}x + \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right)\mathrm{d}x\mathrm{d}y
+ \iint_\Sigma\left(\frac{\partial R}{\partial y} - \frac{\partial Q}{\partial z}\right)\mathrm{d}y\mathrm{d}z + \left(\frac{\partial P}{\partial z} - \frac{\partial R}{\partial x}\right)\mathrm{d}z\mathrm{d}x
\\
- = \oint_\Gamma P\mathrm{d}x + Q\mathrm{d}y + R\mathrm{d}z
+ + \left(\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y}\right)\mathrm{d}x\mathrm{d}y = \oint_\Gamma P\mathrm{d}x + Q\mathrm{d}y + R\mathrm{d}z
\end{multline}
The Stokes formula is an extension of the basic calculus formula in the case of surface integration. It is also an extension of the Green formula. This formula gives the second type of surface integral on the surface block and the second type of curve on the boundary curve Link between points.
\end{definition}