作者：邹云志
页数：350
出版社：世界图书出版公司
出版日期：2015
ISBN：9787510094903
电子书格式：pdf/epub/txt
内容简介
In recently years, more and more Chinese students are going overseas, either as exchange students, or to pursue degrees. At the same time, more and more students are coming from other countries to Chinese universities to further their studies. We’ve noticed that in terms of both knowledge transfer and intercultural communication, the English language has played an indispensable role. Furthermore, it is the interest of these students to have a smooth transition from one system to another, for their credits to transfer, and for them to immerse themselves in the new environment as quickly as possible. To this end, more and more Chinese schools are offering courses delivered bilingually or in English to enhance students’ international outlook. One of the greatest challenges in offering Chinese students a course in English is finding a suitable textbook: the textbook must seriously consider what students have done in their high schools; it must meet the national and local official course standards; and it should resonate with significant international flavors so as to benefit students.
作者简介
教授，应用数学博士，控制科学与工程博士后，毕业于四川大学首届数学基地班。 曾参与编写国家十一五规划教材“Calculus I” 和 ”Calculus II“， 主持和主研各类科学基金5项。
本书特色
（1） 国内第一本国际化数学教材（2） 以学习者为中心的课程内容体系（3）结合国内教育部微积分教学标准和国外同类大学的课程标准（4) 着眼长期规划，3-5年2-3个版本 力争再评上十三五第一最规划教材。
目录
1.1 Overview ofCalculus
1.2 Sets and Numbers
1.2.1 Sets
1.2.2 Numbers
1.2.3 The Least Upper Bound Property
1.2.4 The Extended Real Number System
1.2.5 1ntervals
1.3 Functions
1.3.1 Definition ofa Function
1.3.2 Graph ofa Function
1.3.3 Some Basic Functions and Their Graphs
1.3.4 Building New Functions
1.3.5 Fundamental Elementary Functions
1.3.6 Properties ofFunctions
1.4 Exercises
CHAPTER 2 Limits and Continruty
2.1 Rates ofChange and Derivatives
2.2 Limits of a Function
2.2.1 Definition of a Limit
2.2.2 Properties of Limits of Functions
2.2.3 Limit Laws
2.2.4 One-sided Liruits
2.2.5 Limits Involving Infinity and Asymptotes
2.3 Limits of Sequences
2.3.1 Definitions and Properties
2.3.2 Subsequences
2.4 Squeeze Theorem and Cauchy’s Theorem
2.5 Infinitesimal Functions and Asymptotic Functions
2.6 Continuous and Discontinuous Functions
2.6.1 Continuity and Discontinuity
2.6.2 Continuous Functions
2.6.3 Theorems on Continuous Functions
2.6.4 Uniform Continuity
2.7 Some Proofs in Chapter
2.8 Exercises
CHAPTER 3 I’he Derivative
3.1 Derivative ofa Function at a Point
3.1.1 Instantaneous Rates of Change and Derivatives Revisited
3.1.2 One-sided Derivatives
3.1.3 A Function May Fail to Have a Derivative at a Point
3.2 Derivative as a Function
3.2.1 Graphing the Derivative of a Function
3.2.2 Derivatives of Some Basic Functions
3 .3 Derivative Laws
3.4 Derivative of an Jnverse Function
3.5 Differentiating a Composite Function – The Chain Rule
3.6 Derivatives ofHigher Orders
3.7 Implicit Differentiation
3.8 Functions Defined by Parametric and Polar Equations
3.8.1 Functions Defined by Parametric Equations
3.8.2 Polar Curves
3.9 Related Rates ofChange
3.10 The Tangent Line Approximation and the Differentia
3.10.1 Linearization
3.10.2 Differentials
3.11 Derivative Rules-Summary
3.12 Exercises
CHAPTER 4 Applications of the Derivative
4.1 Extreme Values and The Candidate Theorem
4.2 The Mean Value Theore
4.3 Monotonic Functions and The First Derivative Test
4.3.1 Monotonic Functions
4.3.2 The First Derivative Test
4.4 Extended Mean Value Theorem and the L’Hopital’s Rules
4.4.1 Extended Mean Value Theorem
……
CHAPTER 5 The Definite Integral
CHAPTER 6 Techniques for Integration and Improper Integrals
CHAPTER 7 Applications of the Definite Integral
CHAPTER 8 Infinite Series, Sequences, and Approximations
