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

integral of its curl over the enclosed surface. Stokes' theorem is a special case of the generalized Stokes theorem. In particular, a vector field on R 3 {\displaystyle...

of the generalized Stokes' theorem; however, the latter can be used as an ingredient of its proof. The statement is as follows: Residue theorem: Let U...

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

relativity). Kelvin–Stokes theorem Generalized Stokes theorem Differential form Katz, Victor J. (1979). "The history of Stokes's theorem". Mathematics Magazine...

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

generalizations in this direction is the generalized Stokes theorem (sometimes known as the fundamental theorem of multivariable calculus): Let M be an...

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

theorem can be seen as a consequence of the fundamental theorem of calculus (known by various names in physics such as the Generalized Stokes theorem...

inverse of the derivative of f. The theorem applies verbatim to complex-valued functions of a complex variable. It generalizes to functions from n-tuples (of...

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

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

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′)...

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

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...

special case of Stokes' theorem (surface in R 3 {\displaystyle \mathbb {R} ^{3}} ). In one dimension, it is equivalent to the fundamental theorem of calculus...

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

Poincaré–Hopf theorem (also known as the Poincaré–Hopf index formula, Poincaré–Hopf index theorem, or Hopf index theorem) is an important theorem that is used...

_{\gamma }f\,\mathrm {d} z} ⁠; in light of the Jordan curve theorem and the generalized Stokes' theorem, ⁠ F γ ( z ) {\displaystyle F_{\gamma }(z)} ⁠ is independent...

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

integrating over Ω ( t ) {\displaystyle \Omega (t)} and using generalized Stokes' theorem on the second term, reduces to the three desired terms. Let X...

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...

completely orthogonal planes. Goursat was the first to note that the generalized Stokes theorem can be written in the simple form ∫ S ω = ∫ T d ω {\displaystyle...

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

solved the problem of products of negative numbers by proving the following theorem: "The only multiplication in R which may be considered as an extension...

In mathematics, the mean value theorem (or Lagrange's mean value theorem) states, roughly, that for a given planar arc between two endpoints, there is...

derivative. This provides an essential tool for computation: the generalized Stokes theorem, which allows integration by parts and then elimination of the...

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

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

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...