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 $U$.

Author: mathtuition88

http://mathtuition88.com

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