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:
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:
See also: