本书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。书中还全面讨论了唯一性定理，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。

Part One Infinite Series and Infinite Sequences

Chapter 1 One peratios with Power Series

Additive Unmber Theory,Combinatorial problems,and Applications

Binomial Coefficitents and Related Problem

Differentiation of Power Series

Functional Equations and Power Series

Gaussian Binomial Coefficients

Majorant Series

Chapter 2 Linear Transformations of Series.A Theorem of Cesaro

Triangular Transformations of Sequences into Sequences

More General Transformations of Sequences into Sequences

Transformations of Sequences into Functions,Theorem of Cesaro

Chapter 3 The Structuue of Real Sequences and Series

The Structure of Infinite Sequences

Convergence Exponent

The Maximum Term of a Power Series

Subseries

Rearrangement of the Terms

Distribution of the Sings of the Terms

Chapter 4 Miscellaneous Problems

Evneloping Series

Various Propositions on Real Series and Sequences

Partitions of Sets,Cycles in Permutations

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