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