Green's theorem
Appearance
English
[edit]Etymology
[edit]Named after the mathematician George Green.
Pronunciation
[edit]Noun
[edit]- (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.