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diff --git a/mindmap/divergence theorem.org b/mindmap/divergence theorem.org new file mode 100644 index 0000000..b2c6660 --- /dev/null +++ b/mindmap/divergence theorem.org @@ -0,0 +1,17 @@ +:PROPERTIES: +:ID: 44e65b69-e5d5-464a-b1f3-8a914e1b7e9e +:END: +#+title: divergence theorem +#+author: Preston Pan +#+html_head: <link rel="stylesheet" type="text/css" href="../style.css" /> +#+html_head: <script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script> +#+html_head: <script id="MathJax-script" async src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script> +#+options: broken-links:t + +* 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. |