## green-s-theorem

Noun

(*uncountable*)

- (calculus) A generalization of the fundamental theorem of calculus to the two-dimensional plane, which states that given two scalar fields
*P*and*Q*and a simply connected region*R*, the area integral of derivatives of the fields equals the line integral of the fields, or- .

- (calculus) Letting be a vector field, and this can be restated as
- where is the wedge product, or equivalently, as
- ,

- with the earlier formula resembling Stokes' theorem, and the latter resembling the divergence theorem.