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。
内页插图
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] 下载 mobi epub pdf txt 电子书 格式
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] 下载 mobi pdf epub txt 电子书 格式 2024
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] 下载 mobi epub pdf 电子书
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] mobi epub pdf txt 电子书 格式下载 2024