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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).
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.
Pope John Paul II was the subject of three premature obituaries.. A prematurely reported obituary is an obituary of someone who was still alive at the time of publication. . Examples include that of inventor and philanthropist Alfred Nobel, whose premature obituary condemning him as a "merchant of death" for creating military explosives may have prompted him to create the Nobel Prize; [1 ...
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.
This is a list of lists of deaths of notable people, organized by year. New deaths articles are added to their respective month (e.g., Deaths in February 2025 ) and then linked below. 2025
This is a list of people who died in the last 5 days with an article at the English Wikipedia. For people without an English Wikipedia page see: Wikipedia:Database reports/Recent deaths (red links). Generally updated at least daily, last time: 10:59, 14 February 2025 (UTC).
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 ...
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.