擾動法導論（影印版）

SeriesPreface
Preface
Chapter1:IntroductiontoAsymptoticApproximations
1.1Introduction
1.2Taylor'sTheoremandl'Hospital'sRule
1.3OrderSymbols
1.4AsymptoticApproximations
1.4.1AsymptoticExpansions
1.4.2AccuracyversusConvergenceofanAsymptoticSeries
1.4.3ManipulatingAsymptoticExpansions
1.5AsymptoticSolutionofAlgebraicandTranscendentalEquations
1.6IntroductiontotheAsymptoticSolutionofDifferentialEquations
1.7Uniformity
1.8SymbolicComputing
Chapter2:MatchedAsymptoticExpansions
2.1Introduction
2.2IntroductoryExample
2.3ExampleswithMultipleBoundaryLayers
2.4InteriorLayers
2.5CornerLayers
2.6PartialDifferentialEquations
2.7DifferenceEquations
Chapter3:MultipleScales
3.1Introduction
3.2IntroductoryExample
3.3SlowlyVaryingCoefficients
3.4ForcedMotionNearResonance
3.5BoundaryLayers
3.6IntroductiontoPartialDifferentialEquations
3.7LinearWavePropagation
3.8NonlinearWaves
3.9DifferenceEquations
Chapter4:TheWKBandRelatedMethods
4.1Introduction
4.2IntroductoryExample
4.3TurningPoints
4.4WavePropagationandEnergyMethods
4.5WavePropagationandSlenderBodyApproximations
4.6RayMethods
4.7ParabolicApproximations
4.8DiscreteWKBMethod
Chapter5:TheMethodofHomogenization
5.1Introduction
5.2IntroductoryExample
5.3MultidimensionalProblem:PeriodicSubstructure
5.4PorousFlow
Chapter6:IntroductiontoBifurcationandStability
6.1Introduction
6.2IntroductoryExample
6.3AnalysisofaBifurcationPoint
6.4LinearizedStability
6.5RelaxationDynamics
6.6AnExampleInvolvingaNonlinearPartialDifferentialEquation
6.7BifurcationofPeriodicSolutions
6.8SystemsofOrdinaryDifferentialEquations
AppendixA1:SolutionandPropertiesofTransitionLayerEquations
A1.1AiryFunctions
A1.2ConfluentHypergeometricFunctions
A1.3Higher-OrderTurningPoints
AppendixA2:AsymptoticApproximationsofIntegrals
A2.1Introduction
A2.2Watson'sLemma
A2.3Laplace'sApproximation
A2.4StationaryPhaseApproximation
AppendixA3:NumericalSolutionofNonlinearBoundary-ValueProblems
A3.1Introduction
A3.2Examples
A3.3ComputerCode
References
Index