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First question: $\iint\limits_{\Sigma}\left\{\left(\frac{\partial R}{\partial y}-\frac{\partial Q}{\partial z}\right)\,dy\,dz +\left(\frac{\partial P}{\partial z}-\frac{\partial R}{\partial x}\right)\,dz\,dx +\left (\frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y}\right)\,dx\,dy\right\}$ I am confused about the integral notation: I know that there is double integral, which has variable symbol, at here would be $\Sigma$, that is at the right side to the integral symbol, but I never heard of the integral that places the variable symbol at the center. So, what exactly is this integral, and how is this related to double integral or any type of integral?

Second question: What is double closed integral? How is this integral related to any type of integral?

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It's just a surface integral ($\Sigma$ is the surface). –  anon Jun 27 '12 at 16:52
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