新东方AP考试指定辅导教程：AP微积分电子书

Chapter 1 Introduction of AP Calculus Exam

一、考试报名

二、考试内容

三、考试概况

四、备考资料

五、备考时间安排

Chapter 2 Functions 函数

2.1 Five Basic Elementary Functions 五种基本初等函数

2.1.1 Power Functions 幂函数

2.1.2 Exponential Functions 指数函数

2.1.3 Logarithmic Functions 对数函数

2.1.4 Trigonometric Functions 三角函数

2.1.5 Trigonometric Functions 反三角函数

2.2 Inverse Functions 反函数

2.3 Composite Functions 复合函数

2.4 Parametric Functions 参变量函数

2.5 Polar Functions 极坐标函数

2.6 Vector Functions 向量函数

2.7 Transforming of Functions 函数变换

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Chapter 3 Limit and Continuity 极限与连续

3.1 Definition of a Limit 极限的定义

3.2 Limit Laws 极限（存在）定理

3.3 Rules of Limits 极限的运算法则

3.4 Two Important Limits 两个重要极限

3.5 Application of Limits: Finding Asymptotes 极限的应用：找渐近线

3.6 Continuity 连续

3.6.1 Definition of Continuity 连续的定义

3.6.2 Discontinuity points of a function 函数的不连续点

3.6.3 Theorems of continuous functions 连续函数定理

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Chapter 4 Definition of Derivative 导数定义

4.1 Definition of Derivative 导数的定义

4.1.1 Slope of the line: determined by two points

4.1.2 Definition of Derivative

4.2 One-Sided Derivative 单侧导数

4.3 The Geometric Interpretation of Derivative 导数的几何意义

4.4 The Relation between Differentiability and Continuity 可导与连续的关系

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Chapter 5 Rules for Finding Derivatives 求导法则

5.1 Basic Rules for Finding Derivatives 导数基本运算

5.1.1 The sum, difference, product and quotient rules 加减乘除法则

5.1.2 Basic Differentiation Formulas 基本求导公式（五大函数求导公式）

5.1.3 The Chain Rule 复合函数求导

5.1.4 Logarithmic Differentiation 对数法求导

5.2 High Order Derivatives 高阶导数

5.3 Implicit Differentiation 隐函数求导

5.3.1 Techniques for Implicit Differentiation 隐（函数）求导

5.3.2 High order of Implicit Differentiation 隐函数求高阶导数

5.4 The Derivative of an Inverse Function 反函数求导

5.5 Derivatives of Parametric Functions 参数方程求导

5.6 Derivatives of Polar Functions 极坐标函数求导

5.7 Derivatives of Vector Functions 向量函数求导

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PART 1

PART 2

PART 3

Chapter 6 Applications of Derivatives 导数应用

6.1 Equations of Tangent Lines and Normal Lines 切线和法线方程

6.2 The Mean Value Theorem for Derivatives 微分中值定理

6.3 Related Rates 相关变化率

6.4 Motion 运动学

6.5 Maxima and Minima 最大值和最小值

6.5.1 Basic concepts 基本概念

6.5.2 Two methods for justify whether max or min 判断极值的两个方法

6.5.3 最大值和最小值步骤

6.6 L'Hopital's Rule 洛比达法则

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Chapter 7 Differentials 微分

7.1 Definition of Differential 微分定义

7.2 Linear Approximation 线性估算

7.3 Euler's Method 欧拉法则

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Chapter 8 The Indefinite Integral 不定积分

8.1 The Antiderivative 原函数

8.2 Integration Formulas 积分公式

8.3 U-Substitution 换元法

8.4 Integration by Parts 分部积分

8.5 The Method of Partial Fractions 分式拆分求积分

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Chapter 9 The Definite Integral 定积分

9.1 A Limit of Riemann Sum (Left, Right, Midpoint) 黎曼和的极限

9.2 The First Fundamental Theorem of Calculus 微积分第一基础定理

9.3 The Second Fundamental Theorem of Calculus 微积分第二基础定理

9.4 Improper Integrals 反常积分（广义积分）

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Chapter 10 Applications of Integral 积分应用

10.1 The Mean Value Theorem for Integrals 积分中值定理

10.2 Area 面积

10.2.1 Rectangular Coordinate

10.2.2 Polar Coordinate

10.3 Volume 体积

10.3.1 Disks method and Washers method “圆盘”法和“垫圈”法

10.3.2 Cylindrical Shells 圆柱壳法

10.3.3 Volumes of Solids with Known Cross-sections 已知横截面的固体体积

10.4 Length of A Curve 曲线长度

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Chapter 11 Differential Equations 微分方程

11.1 Separation Variables 可分离变量的微分方程

11.2 Logistic Differential Equation 逻辑斯蒂微分方程

11.3 Slope Fields (Direction Fields) 斜率场

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Chapter 12 Infinite Series 无穷级数

12.1 One Definition for Infinite Series 一个定义

12.2 Two Limits 两个极限

12.3 Three Tests of Series 三大审敛法

12.4 Four Important Series 四种重要级数

12.5 Five formulas of Power Series and Taylor Series 五个重要公式

12.5.1 Power series 幂级数

12.5.2. Taylor Series泰勒级数

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Answers

Chapter 2 Function

Chapter 3 limit and continuity

Chapter 4 Definition of Derivative

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12