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:ID:       44e65b69-e5d5-464a-b1f3-8a914e1b7e9e
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#+title: divergence theorem
#+author: Preston Pan
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* Definition
The [[id:12a2d5b3-f98c-45e5-9107-5560288b5aa8][divergence]] theorem is a generalization of the one-dimensional fundamental theorem of calculus:
\begin{align*}
\int_{V}\vec{\nabla} \cdot \vec{f}(\vec{r})d\tau = \oint_{S}\vec{f}(\vec{r}) \cdot d\vec{a}
\end{align*}
it is a statement about conservation in physical systems: the outflow of force from the inside of a closed boundary has
to be equal to the amount of force at the boundaries.