本书为全英文版。全书共分9个单元，内容包括：实数系统和函数；序列极限；函数极限及连续性；导数和微分；中值定理和导数的应用；不定积分；定积分；定积分的应用；微分方程初步。

本书可作为大学数学系及要求较高的专业的本科生教材，也可作为大学教师教学用书或教学参考书。

本书是为贯彻教育部教学改革精神，实施全英语授课需要而编写。此书书稿在实际教学中已获得广泛好评。其内容包括：实数系统和函数；序列极限；函数极限及连续性；导数和微分；中值定理和导数的应用；不定积分；定积分；定积分的应用；微分方程初步。

本书可作为大学数学系及要求较高的专业的本科生教材，也可作为大学教师教学用书或教学参考书。

Chapter 1 Real number system and functions

 §1.1 Real number system

 §1.2 Inequalities

 §1.3 Functions 

Chapter 2 Sequence Limit

 §2.1 Concept of sequence limit

 §2.2 Properties of convergent sequences

 §2.3 Fundamental theorems of sequenge limit

 §2.4 Upper limit and lower limit of a sequence

Chapter 3 Function limits and continuity 

 §3.1 Concept of function limits 

 §3.2 Properties of function limits

 §3.3 Two important limits

 §3.4 Infinitesimal and infinity

 §3.5 Concept of continuity

 §3.6 Properties of continuous functions

 §3.7 Continuity of primary functions

 §3.8 Uniform continuity

Chapter 4 Derivatives and differentials

 §4.1 Concept of derivatives

 §4.2 Computation of derivatives

 §4.3 Differentials 

 §4.4 Derivatives and differentials of higher order

Chapter 5 Mean value theorems and applications of derivative

 §5.1 Mean value theorems

 §5.2 Monotony and extremum of functions

 §5.3 Graph of a function

 §5.4 L’Hospital rules 

 §5.5 Newton—RaphsOn method

Chapter 6 Indefinite integrals

 §6.1 Concept of indefinite integrals and fundamental

formulas

 §6.2 Techniques of integration

 §6.3 Integration of some special kinds of functions

Chapter 7 Definite integrals

 §7.1 Concept of definite integrals

 §7.2 Properties of definite integrals

 §7.3 The fundamental theorems of caIculus

 §7.4 Integration techniques of definite integrals

 §7.5 Improper integrals

 §7.6 Numerical integration

Chapter 8 Applications of definite integrals 

 §8.1 Applications in geometry

 §8.2 Applications in physics

Chapter 9 Preliminary of differential equations

 §9.1 Basic concepts of differential equations

 §9.2 Differential equations of first—order

 §9.3 Degrading method of second—order differential

equations

 §9.4 Linear differential equations of second—order

 §9.5 Second order linear equations with constant

coefficients

 §9.6 Euler Equation