常微分方程

图书标准信息

• 作者 V.I.Arnold 著
• 出版社 世界图书出版公司
• 出版时间 2003-06
• 版次 1
• ISBN 9787506259460
• 定价 45.00元
• 装帧 平装
• 开本 32开
• 纸张 胶版纸
• 页数 334页

【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