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The divergence theorem can be stated as

$\bigcirc \hspace{-1.3em} \int \hspace{-.8em} \int\limits_{\partial\Omega} dA\,n_i = \iiint\limits_\Omega dV\partial_i$

applied to an arbitrary function (usually a vector valued field) where $\partial\Omega$ is the closed surface of the volume $\Omega\subset\mathbb{R}^3$ and $n_i$ is the $i$th component of the surface normal vector $\vec n$.

Is there a similar correspondence between e.g.

$\bigcirc \hspace{-1.3em} \int \hspace{-.8em} \int\limits_{\partial\Omega} dA\,n_i n_j$

and another volume integral?

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    That looks better! (I didn't actually realise the circle was supposed to go through both integrals).2012-09-05

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