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Divergence theoremDarboux's theoremCauchy's integral theoremBiharmonic equationReynolds transport theoremCalculus on euclidean spaceFundamental theorem of calculusSimons' formulaRicci flowStokes stream functionDirac equation in curved spacetimeSemi-implicit euler methodLefschetz hyperplane theoremLagrange's identityAlgebraic analysisHurewicz theoremD'alembert's formulaLiouville field theoryGeometry and topologyGauge theorySecond covariant derivativeRiemannian geometryGeneral covarianceDuhamel's principleImplicit function theoremGradient theoremGlobal analysisCartan decompositionMultivariable calculusMetric tensorTime-scale calculusExterior covariant derivativeLefschetz fixed-point theoremEuler's theoremMin-max theoremSubderivativeClosed graph theoremEuler's formulaCotangent bundleAffine connectionClosed-subgroup theoremLinear mapCoarea formulaTensor calculusGradientDe rham cohomologyTangent spaceLie bracket of vector fieldsGeometric group theoryK-stabilitySymplectic geometryLie derivativePappus's centroid theoremHartogs's extension theoremGreen's theoremConvex conjugateLagrange inversion theoremKolmogorov continuity theoremTietze extension theoremStickelberger's theoremGeometric flowAbel's identityHodge theorySymplectic manifoldRiemann curvature tensorIsomorphism theoremsDifferential formBott periodicity theoremGeneralizations of the derivativePoisson summation formulaSurface integralCategory theoryChain rulePeano existence theoremLaplace operatorRicci calculusTriple product ruleKolmogorov extension theoremPoisson manifoldEuclidean topologyDifferential geometry of surfacesExact differential equationMultiple-scale analysisIsserlis' theoremPetrov classificationSylvester's formulaMulti-index notationFundamental solutionLaplace expansionSpectral theoryPolarization identityDifferential topologyDifferential structureCalculusFunctional determinantPythagorean trigonometric identityConvolution theoremAdjunction formulaMean value theoremBerezin integral