国外数学名著系列(影印版)线性微分方程的伽罗瓦理论_PDF下载[127MB-百度云](荷)范德帕特(VanderPut,

内容简介

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该书主要论述了线性微分方程的理论知识，包括代数理论、尤其是微分伽罗瓦理论、线性微分方程中的反问题等内容。

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Algebraic Theory1 Picard Vessiot Theory1．1 Differential Rings and Fidlds1．2 Linear Differential Eqations1．3 Picard-Vessiot Extensions1．4 The Differential Galois Group1．5 Liouvillian Extensions2 Differential Operatiors and Differential Modules2．1 The Ring＝k of Differential Operatiors2．2 Constuctions with Differential Modules2．3 Constuctions with Differential Operatiors2．4 Differential Modules and Representations3 Formal Local Theory3．1 Formal Classification of Differential Equations3．2 The Universal Picalr-Vessiot Ring of K3．3 Newton Polygons4 Algorithimc Considerations4．1 Rational and Exponential Solutions4．2 Factoring Linear Operatiors4．3 Liouvillinan Solutions4．4 Finnite Differential Galois GroupsAnalytic Theory……5 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