blob: c50d7b9f5feeac5b97a93ae9fbb5ad61317925d5 (
plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
|
:PROPERTIES:
:ID: 44e65b69-e5d5-464a-b1f3-8a914e1b7e9e
:END:
#+title: divergence theorem
#+author: Preston Pan
#+description: Stokes' the flame.
#+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.
|
