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searching for Stokes' theorem 31 found (155 total)

Calculus on Manifolds (book) (1,170 words) [view diff] no match in snippet view article

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

Residue theorem (3,251 words) [view diff] exact match in snippet view article find links to article

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. The

List of things named after George Gabriel Stokes (148 words) [view diff] exact match in snippet view article find links to article

dynamics Navier–Stokes existence and smoothness Stokes' theorem Kelvin–Stokes theorem Generalized Stokes theorem Stokes operator Stokes phenomenon Stokes (lunar

Faraday's law of induction (4,699 words) [view diff] no match in snippet view article find links to article

electromagnetism. It can also be written in an integral form by the Kelvin–Stokes theorem, thereby reproducing Faraday's law: ∮ ∂ Σ E ⋅ d l = − ∫ Σ ∂ B ∂ t ⋅

Principles of Mathematical Analysis (444 words) [view diff] no match in snippet view article find links to article

and inverse function theorems, differential forms, the generalized Stokes theorem, and the Lebesgue integral. Locascio, Andrew (13 August 2007). "Book

Magnetic flux quantum (1,792 words) [view diff] exact match in snippet view article find links to article

{q}{\hbar }}\mathbf {A} .} Integrating around the hole/loop using Stokes' theorem and ∇ × A = B {\displaystyle \nabla \times \mathbf {A} =B} gives: Φ

Calibrated geometry (921 words) [view diff] exact match in snippet view article find links to article

first equality holds because Σ is calibrated, the second equality is Stokes' theorem (as φ is closed), and the inequality holds because φ is a calibration

List of things named after Lord Kelvin (276 words) [view diff] no match in snippet view article find links to article

pattern Kelvin angle Kelvin’s heat death paradox Zero Kelvin Kelvin–Stokes theorem Kelvin functions Kelvin problem/Kelvin conjecture/Kelvin structure/Kelvin

Hermann Hankel (651 words) [view diff] no match in snippet view article find links to article

Nationality German Alma mater Leipzig University Known for Generalized Stokes theorem Hankel contour Hankel function Hankel matrix Hankel transform Hankel

Math 55 (2,433 words) [view diff] no match in snippet view article find links to article

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

Mimetic interpolation (2,386 words) [view diff] exact match in snippet view article find links to article

interpolation respects the properties of differential forms. In particular, Stokes' theorem ∫ M d ω k ¯ = ∫ ∂ M ω ¯ k {\displaystyle \int _{M}{\overline {d\omega

Lorentz force (8,238 words) [view diff] no match in snippet view article find links to article

sign, the right-hand rule is used, as explained in the article Kelvin–Stokes theorem. The above result can be compared with the version of Faraday's law

Victor J. Katz (824 words) [view diff] exact match in snippet view article find links to article

mathematics from MAA journal; contribution by Katz: The history of Stokes' theorem) with Constantinos Tzanakis: Recent Developments on Introducing a Historical

De Rham cohomology (2,921 words) [view diff] exact match in snippet view article find links to article

{\displaystyle H_{\mathrm {dR} }^{k}(M)\simeq H_{\mathrm {dR} }^{k}(S^{1}).} Stokes' theorem is an expression of duality between de Rham cohomology and the homology

Field line (2,033 words) [view diff] no match in snippet view article find links to article

there will be field lines ending at points in that area. The Kelvin–Stokes theorem shows that field lines of a vector field with zero curl (i.e., a conservative

Mabuchi functional (900 words) [view diff] no match in snippet view article find links to article

which does not depend on the choice of φ{\displaystyle \varphi } by Stokes theorem. Define a differential one-form on the space of Kähler potentials by

Geometrical optics (4,682 words) [view diff] exact match in snippet view article find links to article

-{\tfrac {\varepsilon }{c}}\,\mathbf {E} _{t}=0\end{aligned}}} Using Stokes' theorem in R 4 {\displaystyle \mathbf {R} ^{4}} one can conclude from the first

Ampère's force law (2,912 words) [view diff] exact match in snippet view article find links to article

equivalent way by expanding the vector triple product and applying Stokes' theorem: F 12 = − μ 0 4 π ∫ L 1 ∫ L 2 ( I 1 d ℓ 1 ⋅ I 2 d ℓ 2 ) r ^ 21

Noether's second theorem (2,362 words) [view diff] exact match in snippet view article find links to article

independent variables, the integral total divergence terms vanishes due to Stokes' theorem. Then from the fundamental lemma of the calculus of variations, we

Quantum turbulence (6,270 words) [view diff] no match in snippet view article find links to article

\mathbf {dr} } For a simply-connected surface S {\displaystyle S} , Stokes theorem holds, and the circulation vanishes, as the velocity can be expressed

Siméon Denis Poisson (4,390 words) [view diff] case mismatch in snippet view article find links to article

p. 633. ISBN 0-19-506136-5. Katz, Victor (May 1979). "A History of Stokes' Theorem". Mathematics Magazine. 52 (3): 146–156. doi:10.1080/0025570X.1979

List of Irish people (5,400 words) [view diff] no match in snippet view article find links to article

George Stokes, 1st Baronet (1819–1903) – mathematician, physicist, 'Stokes Theorem' and Stokes-Navier Equations' George Johnstone Stoney (1826–1911) –

Quasiconvexity (calculus of variations) (1,681 words) [view diff] case mismatch in snippet view article

W_{0}^{1,\infty }(B(0,1),\mathbb {R} ^{m\times d})} by the generalised Stokes' Theorem. The determinant det R d × d → R {\displaystyle \det \mathbb {R} ^{d\times

Magnetic field (12,856 words) [view diff] no match in snippet view article find links to article

law. In the case where the bounding surface is stationary, the Kelvin–Stokes theorem can be used to show this equation is equivalent to the Maxwell–Faraday

Hodge star operator (6,814 words) [view diff] exact match in snippet view article find links to article

Hodge star operator not defined). The identity can be proved from Stokes' theorem for smooth forms: 0 = ∫ M d ( η ∧ ⋆ ζ ) = ∫ M ( d η ∧ ⋆ ζ −

Scientific method (20,350 words) [view diff] no match in snippet view article find links to article

Crick and Vand (and independently by Stokes). The Cochran-Crick-Vand-Stokes theorem provided a mathematical explanation for the empirical observation that

BRST quantization (8,856 words) [view diff] no match in snippet view article find links to article

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 as

Faraday paradox (5,655 words) [view diff] no match in snippet view article find links to article

electromagnetism. It can also be written in an integral form by the Kelvin–Stokes theorem. These paradoxes are generally resolved by the fact that an EMF may

Mathematics, science, technology and engineering of the Victorian era (8,295 words) [view diff] exact match in snippet view article find links to article

appears in the study of differential equations. Thomson went on to prove Stokes' theorem, which earned that name after Stokes asked students to prove it in

Timeline of manifolds (1,178 words) [view diff] no match in snippet view article find links to article

Folklore result since c.1850 First conventional publication of the Kelvin–Stokes theorem, in three dimensions, relating integrals over a volume to those on its

Neumann–Poincaré operator (11,016 words) [view diff] no match in snippet view article find links to article

can be checked that TD = 0 by computing directly on powers zn using Stokes theorem to transfer the integral to the boundary. It follows that the conjugate-linear