國外數學名著係列（影印版）33：綫性微分方程的伽羅瓦理論 [Galois Theory of Linear Differential Equations] 下載 mobi epub pdf 電子書 2024

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內容簡介

　　《國外數學名著係列（影印版）33：綫性微分方程的伽羅瓦理論》專門論述綫性微分方程的伽羅瓦理論，涉及諸多方麵：代數理論（尤其是微分伽羅瓦理論）、形式理論、分類、有限項可解性判定算法、單值性、希爾伯特21問題、漸近性和可求和性、反問題以及具正特徵值的綫性微分方程。附錄是《國外數學名著係列（影印版）33：綫性微分方程的伽羅瓦理論》所用到的代數幾何、綫性代數群、層及Tannakian範疇中的一些概念。
　　《國外數學名著係列（影印版）33：綫性微分方程的伽羅瓦理論》將成為談領域所有數學傢和研究生的標準參考書。

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目錄

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

國外數學名著係列（影印版）33：綫性微分方程的伽羅瓦理論 [Galois Theory of Linear Differential Equations] 下載 mobi epub pdf txt 電子書 格式

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