常微分方程
出版时间:
2003-06
版次:
1
ISBN:
9787506259460
定价:
45.00
装帧:
平装
开本:
32开
纸张:
胶版纸
页数:
334页
134人买过
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Thefirsttwochaptersofthisbookhavebeenthoroughlyrevisedandsignificantlyexpanded.Sectionshavebeenaddedonelementarymethodsofintegration(onhomogeneousandinhomogeneousfirst-orderlinearequationsandonhomogeneousandquasi-homogeneousequations),onfirst-orderlinearandquasi-linearpartialdifferentialequations,onequationsnotsolvedforthederivative,andonSturmstheoremsonthezerosofsecond-orderlinearequations.Thustheneweditioncontainsallthequestionsofthecurrentsyllabusinthetheoryofordinarydifferentialequations. Chapter1.BasicConcepts
1.PhaseSpaces
1.ExamplesofEvolutionaryProcesses
2.PhaseSpaces
3.TheIntegralCurvesofaDirectionField
4.ADifferentialEquationanditsSolutions
5.TheEvolutionaryEquationwithaOne-dimensionalPhaseSpace
6.Example:TheEquationofNormalReproduction
Chapter2.BasicTheorems
7.Example:TheExplosionEquation
8.Example:TheLogisticCurve
9.Example:HarvestQuotas
10.Example:HarvestingwithaRelativeQuota
11.EquationswithaMultidimensionalPhaseSpace
12.Example:TheDifferentialEquationofaPredator-PreySystem
Chapter3.LinearSystems
13.Example:AFreeParticleonaLine
14.Example:FreeFall
15.Example:SmallOscillations
16.Example:TheMathematicalPendulum
17.Example:TheInvertedPendulum
18.Example:SmallOscillationsofaSphericalPendulum
19.TheLinearEquationwithaComplexPhaseSpace
20.TheComplexificationofaRealLinearEquation
21.TheClassificationofSingularPointsofLinearSystems
22.TheTopologicalClassificationofSingularPoints
23.StabilityofEquilibriumPositions
24.TheCaseofPurelyImaginaryEigenvalues
25.TheCaseofMultipleEigenvalues
26.Quasi-polynomials
27.NonautonomousLinearEquations
28.LinearEquationswithPeriodicConfficients
29.VariationofConstants
Chapter4.ProofsoftheMainTheorems
30.ContractionMappings
31.ProofoftheTheoremsonExistenceandContinuousDependenceontheInitialConditions
32.TheTheoremonDifferentiability
Chapter5.DifferentialEquationsonManifolds
33.DifferentiableManifolds
34.TheTangentBundle.VectorFieldsonaManiflod
35.ThePhaseFlowDefinedbyaVectorField
36.TheIndicesoftheSingularPointsofaVectorField
ExaminationTopics
SampleExaminationProblems
SubjectIndex
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内容简介:
Thefirsttwochaptersofthisbookhavebeenthoroughlyrevisedandsignificantlyexpanded.Sectionshavebeenaddedonelementarymethodsofintegration(onhomogeneousandinhomogeneousfirst-orderlinearequationsandonhomogeneousandquasi-homogeneousequations),onfirst-orderlinearandquasi-linearpartialdifferentialequations,onequationsnotsolvedforthederivative,andonSturmstheoremsonthezerosofsecond-orderlinearequations.Thustheneweditioncontainsallthequestionsofthecurrentsyllabusinthetheoryofordinarydifferentialequations.
-
目录:
Chapter1.BasicConcepts
1.PhaseSpaces
1.ExamplesofEvolutionaryProcesses
2.PhaseSpaces
3.TheIntegralCurvesofaDirectionField
4.ADifferentialEquationanditsSolutions
5.TheEvolutionaryEquationwithaOne-dimensionalPhaseSpace
6.Example:TheEquationofNormalReproduction
Chapter2.BasicTheorems
7.Example:TheExplosionEquation
8.Example:TheLogisticCurve
9.Example:HarvestQuotas
10.Example:HarvestingwithaRelativeQuota
11.EquationswithaMultidimensionalPhaseSpace
12.Example:TheDifferentialEquationofaPredator-PreySystem
Chapter3.LinearSystems
13.Example:AFreeParticleonaLine
14.Example:FreeFall
15.Example:SmallOscillations
16.Example:TheMathematicalPendulum
17.Example:TheInvertedPendulum
18.Example:SmallOscillationsofaSphericalPendulum
19.TheLinearEquationwithaComplexPhaseSpace
20.TheComplexificationofaRealLinearEquation
21.TheClassificationofSingularPointsofLinearSystems
22.TheTopologicalClassificationofSingularPoints
23.StabilityofEquilibriumPositions
24.TheCaseofPurelyImaginaryEigenvalues
25.TheCaseofMultipleEigenvalues
26.Quasi-polynomials
27.NonautonomousLinearEquations
28.LinearEquationswithPeriodicConfficients
29.VariationofConstants
Chapter4.ProofsoftheMainTheorems
30.ContractionMappings
31.ProofoftheTheoremsonExistenceandContinuousDependenceontheInitialConditions
32.TheTheoremonDifferentiability
Chapter5.DifferentialEquationsonManifolds
33.DifferentiableManifolds
34.TheTangentBundle.VectorFieldsonaManiflod
35.ThePhaseFlowDefinedbyaVectorField
36.TheIndicesoftheSingularPointsofaVectorField
ExaminationTopics
SampleExaminationProblems
SubjectIndex
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