国外数学名著系列(影印版)线性微分方程的伽罗瓦理论

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