# Divergence

In

vector calculus, the

**divergence** is a

vector operator that shows a

vector field's tendency to originate from or converge upon certain points. For instance, in a

vector field that denotes the velocity of water flowing in a draining bathtub, the divergence would have a negative value over the drain because the water flows towards the drain, but does not flow away (if we only consider two dimensions).

Mathematically, the divergence is noted by:

where is the vector differential operator

del and

**F** is the

vector field that the divergence operator is being applied to. Expanded, the notation looks like this:

if

**F** = [F

_{x}, F

_{y}, F

_{z}]

A closer examination of the pattern in the expanded divergence reveals that it can be thought of as being like a dot product between and **F** if was:

and its components were thought to apply their respective derivatives to whatever they are multiplied by.

**See also:**