Symbols:D/Divergence Operator

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Divergence Operator

$\operatorname {div}$

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:

\(\ds \operatorname {div} \mathbf V\) \(:=\) \(\ds \nabla \cdot \mathbf V\)
\(\ds \) \(=\) \(\ds \dfrac {\partial V_x} {\partial x} + \dfrac {\partial V_y} {\partial y} + \dfrac {\partial V_z} {\partial z}\)


$\nabla$ denotes the Del operator
$\cdot$ denotes the dot product
$V_x$, $V_y$ and $V_z$ denote the magnitudes of the components of $\mathbf V$ at $A$ in the directions of the coordinate axes $x$, $y$ and $z$ respectively.

The $\LaTeX$ code for \(\operatorname {div} \mathbf V\) is \operatorname {div} \mathbf V .