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内容简介

　　《国外数学名著系列（影印版）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《国外数学名著系列（影印版）33：线性微分方程的伽罗瓦理论》所用到的代数几何、线性代数群、层及Tannakian范畴中的一些概念。
　　《国外数学名著系列（影印版）33：线性微分方程的伽罗瓦理论》将成为谈领域所有数学家和研究生的标准参考书。

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目录

Algebraic Theory

1 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 Extensions

2 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 Representations

3 Formal Local Theory
3．1 Formal Classification of Differential Equations
3．2 The Universal Picalr-Vessiot Ring of K
3．3 Newton Polygons

4 Algorithimc Considerations
4．1 Rational and Exponential Solutions
4．2 Factoring Linear Operatiors
4．3 Liouvillinan Solutions
4．4 Finnite Differential Galois Groups
Analytic Theory
……
5 Monodromy，the Riemann-Hilbert Problem，and the Differential Galois Group
6 Differential Equations on the Complex Sphere and the Rimann-Hillbert Problem
7 Exact Asymptotics
8 Stokes Phenmenon and Differential Galois Groups
9 Stookes Matrices and Meromorphic Classification
10 Universal Picard-Vessiot Rings and Galois Groups
11 Inverse Problems
12 Modeli for Singular Differential Equations
13 Positive Characteristic
Appendices
A Algebraic Geometry
B Tannakian Categories
C Sheaves and Cohmology
D Partial Differential Equations
Bibliography
List of Notiation
Index

前言/序言

国外数学名著系列（影印版）33：线性微分方程的伽罗瓦理论 [Galois Theory of Linear Differential Equations] 电子书 下载 mobi epub pdf txt

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