Relates a line integral around a simple closed curve in the plane to a double integral over the region it encloses. Named for George Green, it is another special case of the general Stokes' theorem, widely used in two-dimensional vector calculus.
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StatementGreen's theorem relates a line integral taken around a simple closed curve in the plane to a double integral taken over the plane region enclosed by that curve. 1 Classification
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Source MacTutor History of Mathematics, University of St Andrews: George Green (mathematician) (biography)
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Source Green's Theorem (Wikipedia)
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1. Green's Theorem (Wikipedia)
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Green's theorem in the plane relates line integrals around a simple closed curve to double integrals over the regions it encloses.
History section, on Riemann's proof
A proof of the theorem was finally provided in 1851 by Bernhard Riemann in his doctoral dissertation.
Proved By: Bernhard Riemann, Article text
A proof of the theorem was finally provided in 1851 by Bernhard Riemann in his doctoral dissertation.
View the Source MacTutor History of Mathematics, University of St Andrews: George Green (mathematician) (biography)
MacTutor History of Mathematics, University of St AndrewsPrincipal Result Of: George Green (mathematician), Biography, Essay of 1828Quote, Principal Result Of: George Green (mathematician), Biography, Essay of 1828
The formula connecting surface and volume integrals, now known as Green's theorem, was introduced in the work
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