Topic: Green’s Theorem in the Plane

Deriving Boundary Formulas for Area

Divergence as Outward Flux per Unit Area

Area Identities from Green’s Theorem

Choosing Between Boundary and Area Integrals

Curl as Circulation per Unit Area

Computing Circulation from the Curl Density

Computing Outward Flux from the Divergence

Setting Double-Integral Bounds for Green’s Theorem

Deriving Green’s Theorem on Rectangles

Extending the Proof to Simple Planar Regions