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An illustration of Stokes' theorem, with surface Σ, its boundary ∂Σ and the normal vector n.The direction of positive circulation of the bounding contour ∂Σ, and the direction n of positive flux through the surface Σ, are related by a right-hand-rule (i.e., the right hand the fingers circulate along ∂Σ and the thumb is directed along n).
Sir George Gabriel Stokes, 1st Baronet, (/ s t oʊ k s /; 13 August 1819 – 1 February 1903) was an Irish mathematician and physicist.Born in County Sligo, Ireland, Stokes spent all of his career at the University of Cambridge, where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903.
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, [1] is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
Sir George Gabriel Stokes, 1st Baronet, (/ s t oʊ k s /; 13 August 1819 – 1 February 1903) was an Irish mathematician and physicist. Born in County Sligo , Ireland, Stokes spent all of his career at the University of Cambridge , where he was the Lucasian Professor of Mathematics from 1849 until his death in 1903.
In this notation, Stokes' theorem reads as = . In finite element analysis, the first stage is often the approximation of the domain of interest by a triangulation, T. For example, a curve would be approximated as a union of straight line segments; a surface would be approximated by a union of triangles, whose edges are straight line segments ...
Stokes' theorem. It is named after Sir George Gabriel Stokes (1819–1903), although the first known statement of the theorem is by William Thomson (Lord Kelvin) and appears in a letter of his to Stokes. The theorem acquired its name from Stokes' habit of including it in the Cambridge prize examinations. In 1854 he asked his students to prove ...
By Stokes' theorem, the flux of curl or vorticity vectors through a surface S is equal to the circulation around its perimeter, [4] = = = Here, the closed integration path ∂S is the boundary or perimeter of an open surface S , whose infinitesimal element normal d S = n dS is oriented according to the right-hand rule .
The theorem of de Rham shows that this map is actually an isomorphism, a far-reaching generalization of the Poincaré lemma. As suggested by the generalized Stokes' theorem, the exterior derivative is the "dual" of the boundary map on singular simplices.