ABSTRACT
Green’s theorem. If U is an open subset of R2 and Γ is a closed curve such that Γ and Ω (the interior of Γ) both lie in U , then
∮
Γ M dx + N dy =
∫ ∫
( ∂N
∂x − ∂M
∂y
) dxdy
for any functions M and N with continuous first order partial derivatives on U .