Relates the integral of a differential form over the boundary of an oriented manifold to the integral of its exterior derivative over the manifold itself. Named for George Gabriel Stokes, it generalizes and unifies the fundamental theorem of calculus, Green's theorem and the divergence theorem.
Facts
StatementStokes' theorem states, in its usual three-dimensional form, that the total circulation of a vector field around a closed curve equals the total curl of the field through a surface bounded by that curve. 1 Connections
Sources
1. Stokes' Theorem (Wikipedia)
Wikimedia FoundationLead section, statement of the three-dimensional form
In its usual three-dimensional form, it says that the total circulation of a vector field around a closed curve is equal to the total curl of the field through a surface bounded by that curve.
History section, on Thomson's letter to Stokes
The theorem first appears in a letter from William Thomson to George Stokes dated 2 July 1850.
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