Divergence

In Mathematics, the divergence is a vector operator that shows a vector field's tendancy 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:

∇·F

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

∂F_x/∂x + ∂F_y/∂y + ∂F_z/∂z

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:

[∂/∂x, ∂/∂y, ∂/∂z]

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