Irecently 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 ing from other countries to Chinese universities to further their studies. We've noticed that iterms of both knowledge transfer and intercultural munication, the English language has played aindispensable role. Furthermore, it is the interest of these students to have a smooth transitiofrom one system to another, for their credits to transfer, and for them to immerse themselves ithe new environment as quickly as possible. To this end, more and more Chinese schools are offering courses delivered bilingually or iEnglish to enhance students' international outlook.
　　One of the greatest challenges ioffering Chinese students a course iEnglish is finding a suitable textbook: the textbook must seriously consider what students have done itheir 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.

CHAPTER 1 Prereqrusites for Calculus
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 Definitioofa 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 Definitioof 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 oContinuous Functions
2.6.4 Uniform Continuity
2.7 Some Proofs iChapter
2.8 Exercises

CHAPTER 3 I'he Derivative
3.1 Derivative ofa Functioat a Point
3.1.1 Instantaneous Rates of Change and Derivatives Revisited
3.1.2 One-sided Derivatives
3.1.3 A FunctioMay 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 aJnverse Function
3.5 Differentiating a Composite Functio- The ChaiRule
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 Approximatioand 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 MeaValue 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 MeaValue Theorem and the L'Hopital's Rules
4.4.1 Extended MeaValue Theorem
……
CHAPTER 5 The Definite Integral
CHAPTER 6 Techniques for Integratioand Improper Integrals
CHAPTER 7 Applications of the Definite Integral
CHAPTER 8 Infinite Series, Sequences, and Approximations