Green-s-theorem Definition

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.

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(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.

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