Search results for "Fundamental theorem of calculus"

showing 5 items of 5 documents

ON THE FUNDAMENTAL THEOREM OF CALCULUS FOR FRACTAL SETS

2015

The aim of this paper is to formulate the best version of the Fundamental theorem of Calculus for real functions on a fractal subset of the real line. In order to do that an integral of Henstock–Kurzweil type is introduced.

Differentiation under the integral signReal analysisFundamental theoremApplied Mathematicss-SetMathematics::Classical Analysis and ODEss-HK IntegralDifferential calculusTime-scale calculusIntegration by substitutionAlgebraSettore MAT/05 - Analisi MatematicaModeling and SimulationFundamental theorem of calculusFunctions Hs-ACGδ.CalculusGeometry and TopologyGradient theoremMathematicsFractals
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Construction of the ground state in nonrelativistic QED by continuous flows

2006

AbstractFor a nonrelativistic hydrogen atom minimally coupled to the quantized radiation field we construct the ground state projection Pgs by a continuous approximation scheme as an alternative to the iteration scheme recently used by Fröhlich, Pizzo, and the first author [V. Bach, J. Fröhlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys. (2006), doi: 10.1007/s00220-005-1478-3]. That is, we construct Pgs=limt→∞Pt as the limit of a continuously differentiable family (Pt)t⩾0 of ground state projections of infrared regularized Hamiltonians Ht. Using the ODE solved by this family of projections, we sho…

PhysicsIntegrable systemQEDApplied MathematicsGround stateOdeAtom (order theory)Spectral analysisRenormalization groupProjection (linear algebra)Fundamental theorem of calculusQuantum mechanicsLimit (mathematics)Ground stateRenormalization groupAnalysisJournal of Differential Equations
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Exploring Students’ Metacognitive Knowledge: The Case of Integral Calculus

2020

Previous studies of integral calculus have mainly explored students&rsquo

Public AdministrationInterviewMetacognitionPhysical Therapy Sports Therapy and Rehabilitation050105 experimental psychologyEducationmetacognitive knowledgeTaxonomy (general)Fundamental theorem of calculusintegral calculusDevelopmental and Educational PsychologyComputer Science (miscellaneous)Mathematics educationComputingMilieux_COMPUTERSANDEDUCATION0501 psychology and cognitive sciencesMathematics instructionfundamental theorem of calculusKnowledge level05 social sciences050301 educationProcedural knowledgeVDP::Matematikk og Naturvitenskap: 400::Matematikk: 410Computer Science ApplicationsIntegral calculusintegral-area relationshipTheoryofComputation_MATHEMATICALLOGICANDFORMALLANGUAGESmonitoring strategiesTheoryofComputation_LOGICSANDMEANINGSOFPROGRAMSPsychologylcsh:L0503 educationlcsh:EducationEducation Sciences
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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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Stoïlow’s theorem revisited

2020

Stoilow's theorem from 1928 states that a continuous, open, and light map between surfaces is a discrete map with a discrete branch set. This result implies that such maps between orientable surfaces are locally modeled by power maps z -> z(k) and admit a holomorphic factorization. The purpose of this expository article is to give a proof of this classical theorem having readers in mind that are interested in continuous, open and discrete maps. (C) 2019 Elsevier GmbH. All rights reserved. Peer reviewed

continuous open and discrete mappingsPure mathematicsContinuous open and light mappingscontinuous open and light mappingsFundamental theoremPicard–Lindelöf theoremGeneral Mathematics010102 general mathematicsRamsey theoryStoilow's theorem16. Peace & justice01 natural sciencesSqueeze theoremfunktioteoriaFactorizationStoilow’s theoremFundamental theorem of calculusContinuous open and discrete mappings111 Mathematics0101 mathematicsBrouwer fixed-point theoremMathematicsCarlson's theoremExpositiones Mathematicae
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