李群在微分方程中的应用

出版时间：1999-11  出版社：世界图书出版公司  作者：P.J.Olver  页数：513  
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内容概要

This book is devoted to explaining a wide range of applications of continuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems.

书籍目录

Preface to First EditionPreface to Second EditionAcknowledgmentsIntroductionNotes to the ReaderCHAPTER 1 Introduction to Lie Groups  1.1 Manifolds    Change ofCoordinates    Maps Between Manifolds    The Maximal Rank Condition    Submanifolds    Reaular Submanifolds    Implicit Submanifolds    Curves and Connectedness  1.2 Lie Groups    Lie Subgroups    Local Lie Groups    Local Transformation Groups    Orbits  1.3. Vector Fields    Flows    Action on Functions    Differentials    Lie Brackets    Tangent Spaces and Vectors Fields on Submanifolds    Frobenius' Theorem  1.4 LieAlgebras    One-Parameter Subgroups    Subalgebras    The Exponential Map    Lie Algebras of Local Lie Groups    Structure Constants    Commutator Tables    Infinitesimal Group Actions  1.5. Differential Forms    PuIl-Back and Change ofCoordinates    Interior Products    The Differential    The de Rham Complex    Lie Derivatives    Homotopy Operators    Integration and Stokes' Theorem  Notes  ExercisesCHAPTER 2 Symmetry Groups of DifTerential Equations  2.1 Symmetries of Algebraic Equations    Invariant Subsets    Invariant Functions    Infinitesimal Invariance    Local Invariance    Invariants and Functional Dependence    Methods for Constructing Invariants  2.2. Groups and Differential Equations  2.3. Prolongation    Systems of DifTerential Equations    Prolongation ofGroup Actions    Invariance of Differential Equations    Prolongation of Vector Fields    Infinitesimal Invariance    The Prolongation Formula    Total Derivatives    The General Prolongation Formula    Properties of Prolonged Vector Fields    Characteristics of Symmetries  2.4. Calculation of Symmetry Groups  2.5. Integration of Ordinary Differential Equations    First Order Equations    Higher Order Equations    Differential Invariants    Multi-parameter Symmetry Groups    Solvable Groups    Systems of Ordinary Differential Equations  2.6. Nondegeneracy Conditions for Differential Equations    Local Solvability    Invariance Criteria    The Cauchy-Kovalevskaya Theorem    Characteristics    Normal Systems    Prolongation of DifTerential Equations  Notes  ExercisesCHAPTER 3 Group-Invariant Solutions……CHAPTER 4 Symmetry Groups and Conservation LawsCHAPTER 5 Generalized SymmetriesCHAPTER 6 Finite-Dimensional Hamiltonian SystemsCHAPTER 7 Hamiltonian Methods for Evolution EquationsReferencesSymbol IndexAuthor IndexSubject Index

用户评论 (总计9条)

•   看了一小部分（微分方程的对称群），就派上了用场，能不说好吗？内容很丰富，有的你看；一书在手中......前两节简练地（但也有七八十页）介绍了微分流形和向量场；对于了解这些的人这几页算是白买了。
•   非常经典的理论书籍，对学术研究非常有帮助
•   印刷质量总体不错，但偶尔有几页在排版时，存在串页。
•   So detailed, so rich in it worth re*****
•   够看一段时间了
•   书是好书 手感很好 但是书脊有条裂纹 希望工作人员不要因为是书 就只用个袋子装啊 到手的时候都破了……囧啊
•   不错，方程式我研究的重要部分，这本书对我很有用。书本质量也不错。
•   书是老师要求买的，回来后觉得还好
•   部分页面印刷有重影，阅读很不舒服，申请了换货，也收到了邮件，但过了差不多一个月也没有动静。