: Mathématiques: curl

mathematical physics > differential operator > curl

mathematical analysis > functional analysis > operator > differential operator > curl

mathematical physics > vector calculus > vector calculus identities > curl

mathematical analysis > calculus > vector calculus > vector calculus identities > curl

geometry > differential geometry > vector calculus > vector calculus identities > curl

curl

In vector calculus, the curl, also known as rotor, is a vector operator that describes the infinitesimal circulation of a vector field in three-dimensional Euclidean space. The curl at a point in the field is represented by a vector whose length and direction denote the magnitude and axis of the maximum circulation. The curl of a field is formally defined as the circulation density at each point of the field. A vector field whose curl is zero is called irrotational. The curl is a form of differentiation for vector fields. The corresponding form of the fundamental theorem of calculus is Stokes' theorem, which relates the surface integral of the curl of a vector field to the line integral of the vector field around the boundary curve.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Curl_(mathematics))

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