green's theorem

English - English

Definition of green's theorem in English English dictionary

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

\iint_R \left( {\partial Q \over \partial x} - {\partial P \over \partial y}\right) dx \, dy = \oint_{\partial R} P\, dx + Q\, dy .

Letting \vec G = (P, Q) be a vector field, and d\vec l = (dx, dy) this can be restated as

with the earlier formula resembling Stoke's theorem, and the latter resembling the divergence theorem.

Hyphenation

green's the·o·rem

Turkish pronunciation

grinz thîrım

Pronunciation

/ˈgrēnz ˈᴛʜərəm/ /ˈɡriːnz ˈθɪrəm/