李群在微分方程中的应用
1999-11
世界图书出版公司
P.J.Olver
513
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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.
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
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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。