出版社: 科学出版社; 第1版 (2007年1月4日)丛书名: 国外数学名著系列(影印版)精装: 438页开本: 16ISBN: 9787030183019条形码: 9787030183019尺寸: 24 x 16.6 x 2.8 cm重量: 821 g.出版社: 科学出版社; 第1版 (2007年1月4日) 丛书名: 国外数学名著系列(影印版) 精装: 438页 开本: 16 ISBN: 9787030183019 条形码: 9787030183019 尺寸: 24 x 16.6 x 2.8 cm 重量: 821 g 作者:(荷)范德帕特(Van der Put, M.)等 "国外数学名著系列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.附录是本书所用到的代数几何,线性代数群,层及Tannakian范畴中的一些概念. 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