How to remember the Divergence Theorem

The Divergence Theorem:
\displaystyle \int_U\nabla\cdot\mathbf{F}\,dV_n=\oint_{\partial U}\mathbf{F}\cdot\mathbf{n}\,dS_{n-1}

is a rather formidable looking formula that is not so easy to memorise.

One trick is to remember it is to remember the simpler-looking General Stoke’s Theorem.

One can use the general Stoke’s Theorem (\int_{\Omega}d\omega=\int_{\partial\Omega}\omega) to equate the n-dimensional volume integral of the divergence of a vector field \mathbf{F} over a region U to the (n-1)-dimensional surface integral of \mathbf{F} over the boundary of U.


About mathtuition88
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