Intro Calculus微积分初步

本书主要介绍一元微积分和多元微积分的基本内容，其特点是按国内现行教学大纲，全部采用英文编写。全书共分1l章，主要内容包括：变量、函数；极限和连续；导数与微分；中值定理及导数的应用；不定积分；定积分及应用；微分方程；空间向量与平面、直线；多元函数的微分学；多元函数的积分学；级数。本书每章末均附有习题，最后附有习题答案，以供学生复习巩固书中所学内容。
本书可作为高等院校各专业本科生《高等数学》双语教学的教材，还可作为职教、函授大学双语教学的教材及工程技术人员提高科技英语能力的阅读材料。

CHAPTER1 NUMBER，VARIABLE，FUNETION
1.1 REAL NUMBERS.REAL NUMBERS AS POINTS ON A NUMBER SCALE
1.2 THE ABSOLUTE VALUE OF S REAL NUMBER
1.3 VARIABLES AND CONSTANTS
1.4 THE RANGE OF A VARIABLE
1.5 FUNCTION
1.6 ALGEBRAIC FUNCTION
1.6.1 Power function
1.6.2 The rational integral function or poly nomial
1.6.3 Frsctional rational function
1.6.4 Irrational function
1.7 EXPONETIAL，LOGARITHMIC AND TRIGONOMETRIC FUNCTION
1.7.1 General exponential function
1.7.2 Logarithmic function
1.7.3 Trigonometric functions
1.8 ELEMENTARY FUNCTION
1.9 INVERSE FUNCTIONS
EXERCISES ON CHAPTER1
CGHAPTER2 LIMITS AND CONTINUITY OF FUNCTIONS
2.1 THE LIMIT OF AN ORDERED VARIABLE
2.2 THE LIMIT FUNCTION
2.3 PROPERTIES OF THE LIMIT FUNCTION
2.4 A FUNCTION APPROACHES INFINITY
2.5 INFINITESIMALS AND THEIR BASIC PROPERTIES
2.6 BASIC THEOREMS ON LIMITS
2.7 THE LIMOF TWO FUNCTIONS
2.8 CONTINUIY OF FUNCTIONS
2.9 CERTAIN PROPERTIES OF CONTINUOUS FUNCTIONS
EXERCISES ON CHAPTER2
CHARTER3 DERIVE AND DIFFERENTIAL
3.1 VELOCITY OF MOTION
3.2 THE DEFINITION OF A DERIVATIVE
3.3 THE DERIVATIVE OF：A CONSTANT，THE FUNCTION，n A POSITIVE INTEGER
3.4 DERIVATIVES OF：A SUM，APRODUCT AND APUOTIENT
3.5 THE DERIVATIVE OF A COMPOSITE FUNCTION
3.6 DERIVATIVES OF THE FUNCTIONS
3.7 AN INPLICIT FUNCTION AND ITS DIFFERENTIATION
3.8 DERIVATIVESOF A LOGARITHMIC FUNCTION，A GENERAL EXPONENTIAL FUNCTION
3.9 AN INVERSE FUNETION’S DIFFERENTIATION
3.10 BASEC DIFFERENTIATION FORMULAS
3.11 THE DERIVATIVE OF A FUNCTION REPRSENTED PARAMETRICALLY
3.12 THE DIFFERENTIAL
3.13 DERIV ATIVES OF DIFFERENT ORDERS
3.13.1 Derivatives of dlementary functions
3.13.2 Derivatives of implicit functions
3.13.3 Derivatives of functions represented parametrically
3.14 THE EQUATIONS OF A TANGENT AND A NORMAL
3.14.1 The geometric meaning of the differential
3.14.2 The equations of a tangent and a normal
EXERCISES ON CHAPTER3
CHAPTER4 SOME THEOREMS ON DIFFERENTIABLE FUNCTIONS
CHAPTER5 THE INDEFINITE INTEGRAL
CHAPTER6 THE DEFINITE INTEGRAL
CHAPTER7 DIFERENTIAL EQUATIONS
CHAPTER8 VECTORS AND SOLID ANALYTIC GEOMETRY
CHAPTER9 FUNCTIONS OF SEVERAL VARIABLES
CHAPTER10 MRLTIPLE INTEGRALS
CHAPTER11 SERIES
ANSWER TO EXERCISES
REFERENCES