分析中的问题与定理（第1卷）
Douban
Problems and Theorems in Analysis, Volume I
George Pólya / Gábor Szegő
overview
《分析中的问题与定理》主要面向工程科学和应用数学领域的本科生和研究生，因此书中主要强调偏微分程在力学中的应用等内容，各章中的实例研究和每章后的习题均从工程应用中提炼而成。书中还全面讨论了独有性定理，以及极大值原理和极小值原理。本书的根本目的在于引导学生运用力学中的偏微分方程理论建立工程问题模型。
contents
Part One Infinite Series and Infinite Sequences
Chapter 1 One peratios with Power Series
Chapter 2 Linear Transformations of Series.A Theorem of Cesaro
Chapter 3 The Structuue of Real Sequences and Series
Chapter 4 Miscellaneous Problems
Part Two Integration
Chapter 1 The Integral as the Limit of a Sum of Rectangles
Chapter 2 Inequalities
Chapter 3 Some Propertries of Real Functions
Chapter 4 Various Types of Equidistribution
Chapter 5 Functions of Large Numbers
Part Three Functions of One Complex Variable,General Part
Chapter 1 Complex Numbers and Number Sequences
Chapter 2 Mappings and Vector Fields
Chapter 3 Some Geometrical Aspects of Complex Vriables
Chapter 4 Cauchy's Theorem·The Argument Principle
Chapter 5 Sequences of Analytic Functions
Chapter 6 The Maximum Principle
Author Index
Subject Idex
