普通高等教育“十三五”规划教材 普通高等院校数学精品教材 微积分 1 英文版
作者：毛纲源，周海婴著
出版时间： 2017年版
内容简介
毛纲源、周海婴编著的《微积分（Ⅰ英文版普通高等院校数学精品教材）》is generally aimed at first year undergraduate students who major in finance oreconomics. This book strives to provide students and teachers with perspectives and approaches incalculus. The book guides the reader to an appreciation of interrelation among different aspects ofthe subject. It features examples that illustrate key concept as well as exercises that strengthenunderstanding. Chapter 1 provides preliminary knowledge and describes the classical functions. Chapter 2discusses limits and continuity of functions and presents basic facts about continuous functions. InChapter 3， the derivative is defined and the basic rules of differentiation are presented. Chapter 4describes the basic theory of differentiation and Taylor formula. It provides how the derivative usedto discuss properties of functions and apply in economics. Chapter 5 defines anti-derivative andindefinite integral. Fundamental integral formulas， change of variable in integral and integration byparts are also discussed. Chapter 6 introduces， through examples of area and distance， the notion ofthe integral， and the approximate integrals leading to its definition. Fundamental theorem ofcalculus is proved and applications of integrals are provided.
目 录
Chapter 1 Functions
1.1 Preliminary knowledge
1.1.1 Inequalities and their properties
1.1.2 Absolute value and its properties
1.1.3 The range of variable
1.2 Functions
1.2.1 Concept of functions
1.2.2 Features of a function
1.2.3 Inverse functions
1.2.4 Composite functions
1.2.5 Elementary functions
1.2.6 Non-elementary functions
1.2.7 Implicit functions
Exercise 1
Chapter 2 Limit and Continuity
2.1 Limit
2.1.1 Definition of a sequence
2.1.2 Deive definition of limit of a sequence
2.1.3 Quantitative definition of limit of a sequence
2.2 Limits of functions
2.2.1 Definition of finite limits of functions as x→x0
2.2.2 Definition of infinite limits of functions as x→x0
2.2.3 Limits of functions as independent variable tending to infinity
2.2.4 Left limit and right limit
2.2.5 The properties of limits of functions
2.2.6 Operation rules of limits
2.2.7 Criteria of existence of limits and two important limits
2.2.8 Infinitesimal, infinity and their basic properties
2.2.9 Simple application of limit in economics
2.3 Continuity of functions
2.3.1 Continuity
2.3.2 Discontinuous points of a function
2.3.3 Operations and properties of continuous functions
2.3.4 Continuity of elementary functions
2.3.5 Continuity of the inverse functions
2.3.6 Properties of continuous functions on closed interval
Exercise 2
Chapter 3 Derivative and differential
3.1 Concept of derivative
3.1.1 Introduction of derivative
3.1.2 Definition of derivative
3.1.3 Left-hand derivative and righthand derivative
3.1.4 The relationship between differentiability and continuity of functions
3.1.5 Applying the definition of derivative to find derivatives
3.1.6 Geometric interpretation of derivative
3.2 Rules of finding derivatives
3.2.1 Four arithmetic operation rules of derivatives
3.2.2 Derivative rules of composite functions
3.2.3 Derivative rules of inverse functions
3.2.4 Derivative rules of implicit functions
