Definitions from Wiktionary (Green's theorem)

▸ noun:  (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
▸ noun:  (calculus) Letting ⃑G=(P,Q) be a vector field, and d⃑l=(dx,dy) this can be restated as


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