常微分方程基础理论(影印版)天元基金影印数学丛书正版现货
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九品
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作者[美]赫斯赫(Hsieh P.F.) 著
出版社高等教育出版社
出版时间2007-07
版次1
装帧平装
货号仓库箱a08
上书时间2024-10-19
商品详情
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图书标准信息
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作者
[美]赫斯赫(Hsieh P.F.) 著
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出版社
高等教育出版社
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出版时间
2007-07
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版次
1
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ISBN
9787040220667
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定价
37.40元
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装帧
平装
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开本
16开
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纸张
胶版纸
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页数
468页
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字数
500千字
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正文语种
英语
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丛书
天元基金影印数学丛书
- 【内容简介】
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本书为开展常微分方程研究工作的读者提供必要的准备知识,可作为本科高年级和研究生常微分方程课程教材。
本书内容分为四部分:第一部分(第一、二、三章)的内容包括解的存在性、唯一性、对数据的光滑依赖性,以及解的非唯一性;第二部分(第四、六、七章)讨论线性常微分方程,书中用矩阵的S-N分解代替Jordan分解,前者的计算较后者更容易;第三部分(第八、九、十章)讨论非线性常微分方程的稳定性、渐近稳定性等几何理论;第四部分(第五、十一,十二、十三章)讨论常微分方程的幂级数解,包括线性常微分方程的奇点分类及非线性常微分方程当参数或自变量趋向某奇点时的渐近解等。
- 【目录】
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Preface
ChapterⅠ.FundamentalTheoremsofOrdinaryDifferentialEquations
Ⅰ-1.ExistenceanduniquenesswiththeLipschitzcondition
Ⅰ-2.ExistencewithouttheLipschitzcondition
Ⅰ-3.Someglobalpropertiesofsolutions
Ⅰ-4.Analyticdifferentialequations
ExercisesⅠ
ChapterⅡ.DependenceonData
Ⅱ-1.Continuitywithrespecttoinitialdataandparameters
Ⅱ-2.Differentiability
ExercisesⅡ
ChapterⅢ.Nonuniqueness
Ⅲ-1.Examples
Ⅲ-2.TheKnesertheorem
Ⅲ-3.SolutioncurvesontheboundaryofR(A)
Ⅲ-4.Maximalandminimalsolutions
Ⅲ-5.Acomparisontheorem
Ⅲ-6.Sufficientconditionsforuniqueness
ExercisesⅢ
ChapterⅣ.GeneralTheoryofLinearSystems
Ⅳ-1.Somebasicresultsconcerningmatrices
Ⅳ-2.Homogeneoussystemsoflineardifferentialequations
Ⅳ-3.Homogeneoussystemswithconstantcoefficients
Ⅳ-4.Systemswithperiodiccoefficients
Ⅳ-5.LinearHamiltoniansystemswithperiodiccoefficients
Ⅳ-6.Nonhomogeneousequations
Ⅳ-7.Higher-orderscalarequations
ExercisesⅣ
ChapterⅤ.SingularitiesoftheFirstKind
Ⅴ-1.Formalsolutionsofanalgebraicdifferentialequation
Ⅴ-2.Convergenceofformalsolutionsofasystemofthefirstkind
Ⅴ-3.TheS-Ndecompositionofamatrixofinfiniteorder
Ⅴ-4.TheS-Ndecompositionofadifferentialoperator
Ⅴ-5.Anormalformofadifferentialoperator
Ⅴ-6.Calculationofthenormalformofadifferentialoperator
Ⅴ-7.Classificationofsingularitiesofhomogeneouslinearsystems
ExercisesⅤ
ChapterⅥ.Boundary-ValueProblemsofLinearDifferentialEquationsoftheSecond-Order
Ⅵ-1.Zerosofsolutions
Ⅵ-2.Sturm-Liouvilleproblems
Ⅵ-3.Eigenvalueproblems
Ⅵ-4.Eigenfunctionexpansions
Ⅵ-5.Jostsolutions
Ⅵ-6.Scatteringdata
Ⅵ-7.Refiectionlesspotentials
Ⅵ-8.Constructionofapotentialforgivendata
Ⅵ-9.Differentialequationssatisfiedbyreflectionlesspotentials
Ⅵ-10.Periodicpotentials
ExercisesⅥ
ChapterⅦ.AsymptoticBehaviorofSolutionsofLinearSystems
Ⅶ-1.Liapounoffstypenumbers
Ⅶ-2.Liapounoffstypenumbersofahomogeneouslinearsystem
Ⅶ-3.CalculationofLiapounoffstypenumbersofsolutions
Ⅶ-4.Adiagonalizationtheorem
Ⅶ-5.Systemswithasymptoticallyconstantcoefficients
Ⅶ-6.AnapplicationoftheFloquettheorem
ExercisesⅦ
ChapterⅧ.Stability
Ⅷ-1.Basicdefinitions
Ⅷ-2.Asufficientconditionforasymptoticstability
Ⅷ-3.Stablemanifolds
Ⅷ-4.Analyticstructureofstablemanifolds
Ⅷ-5.Two-dimensionallinearsystemswithconstantcoefficients
Ⅷ-6.AnalyticsystemsinR2
Ⅷ-7.Perturbationsofanimpropernodeandasaddlepoint
Ⅷ-8.Perturbationsofapropernode
Ⅷ-9.Perturbationofaspiralpoint
Ⅷ-10.Perturbationofacenter
ExercisesⅧ
ChapterⅨ.AutonomousSystems
Ⅸ-1.Limit-invariantsets
Ⅸ-2.Liapounoffsdirectmethod
Ⅸ-3.Orbitalstability
Ⅸ-4.ThePoincare-Bendixsontheorem
Ⅸ-5.IndicesofJordancurves
ExercisesⅨ
ChapterⅩ.TheSecond-OrderDifferentialEquation(d2x)/(dt2)+h(x)*(dx)/(dt)+g(x)=0
Ⅹ-1.Two-pointboundary-valueproblems
Ⅹ-2.ApplicationsoftheLiapounofffunctions
Ⅹ-3.Existenceanduniquenessofperiodicorbits
Ⅹ-4.MultipliersoftheperiodicorbitofthevanderPolequation
Ⅹ-5.ThevanderPolequationforasmallε>0
Ⅹ-6.ThevanderPolequationforalargeparameter
Ⅹ-7.AtheoremduetoM.Nagumo
Ⅹ-8.Asingularperturbationproblem
ExercisesⅩ
ChapterⅪ.AsymptoticExpansions
Ⅺ-1.AsymptoticexpansionsinthesenseofPoincare
Ⅺ-2.Gevreyasymptotics
Ⅺ-3.FlatfunctionsintheGevreyasymptotics
Ⅺ-4.BasicpropertiesofGevreyasymptoticexpansions
Ⅺ-5.ProofofLemmaⅪ-2-6
ExercisesⅪ
ChapterⅫ.AsymptoticExpansionsinaParameter
Ⅻ-1.Anexistencetheorem
Ⅻ-2.Basicestimates
Ⅻ-3.ProofofTheoremⅫ-1-2
Ⅻ-4.Ablock-diagonalizationtheorem
Ⅻ-5.Gevreyasymptoticsolutionsinaparameter
Ⅻ-6.Analyticsimplificationinaparameter
ExercisesⅫ
ChapterⅩⅢ.SingularitiesoftheSecondKind
ⅩⅢ-1.Anexistencetheorem
ⅩⅢ-2.Basicestimates
ⅩⅢ-3.ProofofTheoremⅩⅢ-1-2
ⅩⅢ-4.Ablock-diagonalizationtheorem
ⅩⅢ-5.Cyclicvectors(AlemmaofP.Deligne)
ⅩⅢ-6.TheHukuhara-Turrittintheorem
ⅩⅢ-7.Ann-th-orderlineardifferentialequationatasingularpointofthesecondkind
ⅩⅢ-8.Gevreypropertyofasymptoticsolutionsatanirregularsingularpoint
ExercisesⅩⅢ
References
Index
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