线性微分方程的伽罗瓦理论

作者简介

《国外数学名著系列33:线性微分方程的伽罗瓦理论》专门论述线性微分方程的伽罗瓦理论，涉及诸多方面：代数理论（尤其是微分伽罗瓦理论）、形式理论、分类、有限项可解性判定算法、单值性、希尔伯特21问题、渐近性和可求和性，反问题以及具正特征值的线性微分方程。附录是本书所用到的代数几何、线性代数群、层及Tannakian范畴中的一些概念。

书籍目录

Algebraic Theory1 Picard Vessiot Theory  1.1  Differential Rings and Fidlds  1.2  Linear Differential Eqations  1.3  Picard-Vessiot Extensions  1.4  The Differential Galois Group  1.5  Liouvillian Extensions2  Differential Operatiors and Differential Modules  2.1 The Ring＝k of Differential Operatiors  2.2  Constuctions with Differential Modules  2.3  Constuctions with Differential Operatiors  2.4  Differential Modules and Representations3  Formal Local Theory  3.1  Formal Classification of Differential Equations  3.2  The Universal Picalr-Vessiot Ring of K  3.3  Newton Polygons4 Algorithimc Considerations  4.1  Rational and Exponential Solutions  4.2  Factoring Linear Operatiors  4.3  Liouvillinan Solutions  4.4  Finnite Differential Galois GroupsAnalytic Theory5 Monodromy,the Riemann-Hilbert Problem,and the Differential Galois Group6 Differential Equations on the Complex Sphere and the Rimann-Hillbert Problem7 Exact Asymptotics8 Stokes Phenmenon and Differential Galois Groups9 Stookes Matrices and Meromorphic Classification10 Universal Picard-Vessiot Rings and Galois Groups11 Inverse Problems12 Modeli for Singular Differential Equations13 Positive CharacteristicAppendicesA Algebraic GeometryB Tannakian CategoriesC Sheaves and CohmologyD Partial Differential EquationsBibliographyList of NotiationIndex

编辑推荐

《国外数学名著系列33:线性微分方程的伽罗瓦理论》将成为该领域所有数学家和研究生的标准参考书。

内容概要

作者:(荷)范德帕特(Van der Put、 M.)等

图书封面

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