Definition:Divergence Operator/Geometrical Representation

Definition
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:


 * $\operatorname {div} \mathbf V = \dfrac {\partial V_x} {\partial x} + \dfrac {\partial V_y} {\partial y} + \dfrac {\partial V_z} {\partial z}$

where:
 * $V_x$, $V_y$ and $V_z$ denote the magnitudes of the components of $\mathbf V$ in the directions of the coordinate axes $x$, $y$ and $z$ respectively.

Also see

 * Justification for Geometrical Representation of Divergence Operator