: Matemáticas: Helmholtz's theorem

mathematical physics > vector calculus > Helmholtz's theorem

mathematical analysis > calculus > vector calculus > Helmholtz's theorem

geometry > differential geometry > vector calculus > Helmholtz's theorem

Helmholtz's theorem

In physics and mathematics, in the area of vector calculus, Helmholtz's theorem, also known as the fundamental theorem of vector calculus, states that any sufficiently smooth, rapidly decaying vector field in three dimensions can be resolved into the sum of an irrotational (curl-free) vector field and a solenoidal (divergence-free) vector field; this is known as the Helmholtz decomposition or Helmholtz representation. It is named after Hermann von Helmholtz.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Helmholtz_decomposition)

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