Mathematics
Green's Theorem and Its Relation to Flux and Circulation
Quick fact
Green's theorem is a two-dimensional analogue of the Fundamental Theorem of Calculus: instead of subtracting antiderivative values at two endpoints, you relate the total circulation or flux around a closed curve to a single double integral over the area it encloses.
Why this is interesting
You've seen that the area of a shape can be found by integrating over its interior, but what if you only knew the flow along its boundary? It turns out that a single line integral can reveal secrets of the whole region inside.