Definition:Divergence Operator/Integral Form

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Let $R$ be a region of space embedded in a Cartesian coordinate frame.

Let $\mathbf V$ be a vector field acting over $R$.

The divergence of $\mathbf V$ at a point $A$ in $R$ is defined as:

$\ds \operatorname {div} \mathbf V := \lim_{\delta \tau \mathop \to 0} \dfrac {\int_S \mathbf V \cdot \d S} {\delta \tau}$


$S$ is the surface of a volume element $\delta \tau$ containing $A$
$\cdot$ denotes the dot product
$\int_S$ denotes the surface integral over $S$.

Also see

  • Results about divergence can be found here.