Search results for "Kelvin–Stokes theorem"

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The Riesz Representation Theorem and Extension of Vector Valued Additive Measures

2001

Discrete mathematicsPure mathematicsM. Riesz extension theoremRiesz representation theoremKelvin–Stokes theoremRiesz potentialApplied MathematicsBanach spaceExtension (predicate logic)Characterization (mathematics)AnalysisMathematicsJournal of Mathematical Analysis and Applications
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The General Stokes’s Theorem

2012

Let ω be a differential form of degree k - 1 and class C 1 in a neighborhood of a compact regular k-surface with boundary M of class C 2. The general Stokes’s theorem gives a relationship between the integral of ω over the boundary of M and the integral of the exterior differential dω over M. It can be viewed as a generalization of Green’s theorem to higher dimensions, and it plays a role not unlike that of the fundamental theorem of calculus in an elementary course of analysis. Particular cases of the general Stokes’s theorem that are of great importance are the divergence theorem, which relates a triple integral with a surface integral and what we know as the classical Stokes’s theorem, w…

Pure mathematicsPicard–Lindelöf theoremKelvin–Stokes theoremFundamental theorem of calculusSurface integralResidue theoremMathematical analysisLine integralDivergence theoremExterior derivativeMathematics
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