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divergence theorem

Table of Contents

1. Definition

The divergence theorem is a generalization of the one-dimensional fundamental theorem of calculus:

∫V∇→⋅f→(r→)dτ=∮Sf→(r→)⋅da→\begin{aligned}\int_{V}\vec{\nabla} \cdot \vec{f}(\vec{r})d\tau = \oint_{S}\vec{f}(\vec{r}) \cdot d\vec{a}\end{aligned}

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.