geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, is a statement...

along ∂Σ and the thumb is directed along n. Stokes' theorem is a special case of the generalized Stokes theorem. In particular, a vector field on R 3 {\displaystyle...

residue theorem should not be confused with special cases of the generalized Stokes' theorem; however, the latter can be used as an ingredient of its proof...

theorem of calculus, the divergence theorem, Green's theorem, and Stokes' theorem as special cases of a single general result, the generalized Stokes...

Notice the striking similarity between this statement and the generalized Stokes’ theorem, which says that the integral of any compactly supported differential...

manifolds embedded in Euclidean space, and as corollaries of the generalized Stokes theorem on manifolds-with-boundary. The book culminates with the statement...

The proof of Cauchy's integral theorem for higher dimensional spaces relies on the using the generalized Stokes theorem on the quantity G(r, r′) f(r′)...

plane region D bounded by C. It is the two-dimensional special case of Stokes' theorem. Let C be a positively oriented, piecewise smooth, simple closed curve...

discussion of the implicit and inverse function theorems, differential forms, the generalized Stokes theorem, and the Lebesgue integral. Locascio, Andrew...

}(z)=F_{0}+\int _{\gamma }f\,dz;} in light of the Jordan curve theorem and the generalized Stokes' theorem, Fγ(z) is independent of the particular choice of path...

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are...

it is seen that these four theorems are specific incarnations of a more general theorem, the generalized Stokes' theorem, which applies to the integration...

point. The theorem also gives a formula for the derivative of the inverse function. In multivariable calculus, this theorem can be generalized to any continuously...

a natural, metric-independent generalization of Stokes' theorem, Gauss's theorem, and Green's theorem from vector calculus. If a differential k-form is...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

integrating over Ω ( t ) {\displaystyle \Omega (t)} and using generalized Stokes' theorem on the second term, correspond to the three terms in the formula...

(multi)linear maps. These topics typically culminated in the proof of the generalized Stokes theorem, though, time permitting, other relevant topics (e.g. category...

Navier–Stokes equations, see section on fluid dynamics Navier–Stokes existence and smoothness Stokes' theorem Kelvin–Stokes theorem Generalized Stokes theorem...

such functions that represent conservative vector fields. (The generalized Stokes' theorem has preserved integrability.) First, note the curl of all such...

theorem, strongly geometric in character, was by James Gregory (1638–1675). Isaac Barrow (1630–1677) proved a more generalized version of the theorem...

hence the above limits exist and are real numbers. This generalized version of the theorem is sufficient to prove convexity when the one-sided derivatives...

symmetry under such transformations. This is the seed idea generalized in Noether's theorem. Several alternative methods for finding conserved quantities...

In physics and mathematics, the Helmholtz decomposition theorem or the fundamental theorem of vector calculus states that any sufficiently smooth, rapidly...

In calculus, Taylor's theorem gives an approximation of a k {\textstyle k} -times differentiable function around a given point by a polynomial of degree...

calculus, and more generally differential geometry, Stokes' theorem (also called the generalized Stokes' theorem) is a statement about the integration of differential...

and Stokes' theorem simultaneously generalizes the three theorems of vector calculus: the divergence theorem, Green's theorem, and the Kelvin-Stokes theorem...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

They can be used to formulate a very general Stokes' theorem. Beppo-Levi space Dirac delta function Generalized eigenfunction Distribution (mathematics) Hyperfunction...

derivative. And we obtain an essential tool for computation: the generalized Stokes theorem, which allows us to integrate by parts and drop the surface term...

the implicit function theorem. Ulisse Dini (1845–1918) generalized the real-variable version of the implicit function theorem to the context of functions...