非线性泛函分析及其应用/第4卷《在数学物理中的应用》

《非线性泛函分析及其应用,第4卷,在数学物理中的应用》的写作起点很低，具备本科数学水平就可以读。

作者：(德国)宰德勒

Preface
Translator'sPreface
INTRODUCTION
MathematicsandPhysics
APPLICATIONSINMECHANICS
CHAPTER58
BasicEquationsofPointMechanics
58.1.Notations
58.2.LeverPrincipleandStabilityoftheScales
58.3.Perspectives
58.4.Kepler'sLawsandaLookattheHistoryofAstronomy
58.5.Newton'sBasicEquations
58.6.ChangesoftheSystemofReferenceandtheRoleofInertialSystems
58.7.GeneralPointSystemandItsConservedQuantities
58.8.Newton'sLawofGravitationandCoulomb'sLawofElectrostatics
58.9.ApplicationtotheMotionofPlanets
58.10.Gauss'PrincipleofLeastConstraintandtheGeneralBasic
EquationsofPointMechanicswithSideConditions
58.11.PrincipleofVirtualPower
58.12.EquilibriumStatesandaGeneralStabilityPrinciple
58.13.BasicEquationsoftheRigidBodyandtheMainTheoremaboutthe
MotionoftheRigidBodyandItsEquilibrium
58.14.FoundationoftheBasicEquationsoftheRigidBody
58.15.PhysicalModels,theExpansionoftheUniverse,andItsEvolution
aftertheBigBang
58.16.LegendreTransformationandConjugateFunctionals
58.17.LagrangeMultipliers
58.18.PrincipleofStationaryAction
58.19.TrickofPositionCoordinatesandLagrangianMechanics
58.20.HamiltonianMechanics
58.21.PoissonianMechanicsandHeisenberg'sMatrixMechanicsin
QuantumTheory
58.22.PropagationofAction
58.23.Hamilton-JacobiEquation
58.24.CanonicalTransformationsandtheSolutionoftheCanonical
EquationsviatheHamilton-JacobiEquation
58.25.LagrangeBracketsandtheSolutionoftheHamilton-Jacobi
EquationviatheCanonicalEquations
58.26.Initial-ValueProblemfortheHamiiton-JacobiEquation
58.27.DimensionAnalysis

CHAPTER59
DualismBetweenWaveandParticle,PreviewofQuantumTheory,
andElementaryParticles
59.1.PlaneWaves
59.2.Polarization
59.3.DispersionRelations
59.4.SphericalWaves
59.5.DampedOscillationsandtheFrequency-TimeUncertaintyRelation
59.6.DecayofParticles
59.7.CrossSectionsforElementaryParticleProcessesandtheMain
ObjectivesinQuantumFieldTheory
59.8.DualismBetweenWaveandParticleforLight
59.9.WavePacketsandGroupVelocity
59.10.FormulationofaPal:ticleTheoryforaClassicalWaveTheory
59.11.MotivationoftheSchrfdingerEquationandPhysicalIntuition
59.12.FundamentalProbabilityInterpretationofQuantumMechanics
59.13.MeaningofEigenfunctionsinQuantumMechanics
59.14.MeaningofNonnormalizedStates
59.15.SpecialFunctionsinQuantumMechanics
59.16.SpectrumoftheHydrogenAtom
59.17.FunctionalAnalyticTreatmentoftheHydrogenAtom
59.18.HarmonicOscillatorinQuantumMechanics
59.19.Heisenberg'sUncertaintyRelation
59.20.PauliPrinciple,Spin,andStatistics
59.21.QuantizationofthePhaseSpaceandStatistics
59.22.PauliPrincipleandthePeriodicSystemoftheElements
59.23.ClassicalLimitingCaseofQuantumMechanicsandthe
WKBMethodtoComputeQuasi-ClassicalApproximations
59.24.Energy-TimeUncertaintyRelationandElementaryParticles
59.25.TheFourFundamentalInteractions
59.26.StrengthoftheInteractions
APPLICATIONSINELASTICITYTHEORY

CHAPTER60
ElastoplasticWire
60.1.ExperimentalResult
60.2.ViscoplasticConstitutiveLaws
60.3.Elasto-ViscoplasticWirewithLinearHardeningLaw
60.4.Quasi-StaticalPlasticity
60.5.SomeHistoricalRemarksonPlasticity

CHAPTER61
BasicEquationsofNonlinearElasticityTheory
61.1.Notations
61.2.StrainTensorandtheGeometryofDeformations
61.3.BasicEquations
61.4.PhysicalMotivationoftheBasicEquations
61.5.ReducedStressTensorandthePrincipleofVirtualPower
61.6.AGeneralVariationalPrinciple(Hyperelasticity)
61.7.ElasticEnergyoftheCuboidandConstitutiveLaws
61.8.TheoryoflnvariantsandtheGeneralStructureofConstitutiveLaws
andStoredEnergyFunctions
61.9.ExistenceandUniquenessinLinearElastostatics(Generalized
Solutions)
61.10.ExistenceandUniquenessinLinearElastodynamics(Generalized
Solutions)
61.11.StronglyEllipticSystems
61.12.LocalExistenceandUniquenessTheoreminNonlinearElasticityvia
theImplicitFunctionTheorem
61.13.ExistenceandUniquenessTheoreminLinearElastostatics(Classical
Solutions)
61.14.StabilityandBifurcationinNonlinearElasticity
61.15.TheContinuationMethodinNonlinearElasticityandan
ApproximationMethod
61.16.ConvergenceoftheApproximationMethod

CHAPTER62
MonotonePotentialOperatorsandaClassofModelswithNonlinear
Hooke'sLaw,DualityandPlasticity,andPolyconvexity
62.1.BasicIdeas
62.2.Notations
62.3.PrincipleofMinimalPotentialEnergy,Existence,andUniqueness
62.4.PrincipleofMaximalDualEnergyandDuality
62.5.ProofsoftheMainTheorems
62.6.ApproximationMethods
62.7.ApplicationstoLinearElasticityTheory
62.8.ApplicationtoNonlinearHenckyMaterial
62.9.TheConstitutiveLawforQuasi-StaticalPlasticMaterial
62.10.PrincipleofMaximalDualEnergyandtheExistenceTheoremfor
LinearQuasi-StaticalPlasticity
62.11.DualityandtheExistenceTheoremforLinearStaticalPlasticity
62.12.CompensatedCompactness
62.13.ExistenceTheoremforPolyconvexMaterial
62.14.ApplicationtoRubberlikeMaterial
62.15.ProofofKorn'sInequality
62.16.LegendreTransformationandtheStrategyoftheGeneralFriedrichs
DualityintheCalculusofVariations
62.17.ApplicationtotheDirichletProblem(TrefftzDuality)
62.18.ApplicationtoElasticity

CHAPTER63
VariationalInequalitiesandtheSignoriniProblemforNonlinear
Material
63.1.ExistenceandUniquenessTheorem
63.2.PhysicalMotivation

CHAPTER64
BifurcationforVariationalInequalities
64.1.BasicIdeas
64.2.QuadraticVariationalInequalities
64.3.LagrangeMultiplierRuleforVariationalInequalities
64.4.MainTheorem
64.5.ProofoftheMainTheorem
64.6.ApplicationstotheBendingofRodsandBeams
64.7.PhysicalMotivationfortheNonlinearRodEquation
64.8.ExplicitSolutionoftheRodEquation

CHAPTER65
PseudomonotoneOperators,Bifurcation,andthevonKtrmhnPlate
Equations
65.1.BasicIdeas
65.2.Notations
65.3.ThevonKarmamPlateEquations
65.4.TheOperatorEquation
65.5.ExistenceTheorem
65.6.Bifurcation
65.7.PhysicalMotivationofthePlateEquations
65.8.PrincipleofStationaryPotentialEnergyandPlateswithObstacles

CHAPTER66
ConvexAnalysis,MaximalMonotoneOperators,andElasto-
ViscoplasticMaterialwithLinearHardeningandHysteresis
66.1.AbstractModelforSlowDeformationProcesses
66.2.PhysicalInterpretationoftheAbstractModel
66.3.ExistenceandUniquenessTheorem
66.4.Applications
……
CHAPTER67
CHAPTER68
CHAPTER69
CHAPTER70
CHAPTER71
CHAPTER72
CHAPTER73
CHAPTER74
CHAPTER75
CHAPTER76
CHAPTER77
CHAPTER78
CHAPTER79
Index