Chapter 1 Introduction of AP Calculus Exam AP微积分考试介绍
Chapter 2 Functions函数
2.1 Five Basic Elementary Functions五种基本初等函数
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
(Practice Problems?课后练习)
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
(Practice Problems?课后练习)
Chapter 4 Definition of Derivative导数定义
4.1 Definition of Derivative导数的定义
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
(Practice Problems?课后练习)
Chapter 5 Rules for Finding Derivatives求导法则
5.1 Basic Rules for Finding Derivatives导数基本运算
5.2 High Order Derivatives高阶导数
5.3 Implicit Differentiation“隐函数”求导
5.4 The Derivative of an Inverse Function反函数求导
5.5 Derivatives of Parametric Functions参数方程求
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
(Practice Problems?课后练习)
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*大值和*小值
6.6 L’Hopital’s Rule洛比达法则
(Practice Problems?课后练习)
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
(Practice Problems?课后练习)
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
(Practice Problems?课后练习)
Chapter 9 The Definite Integral定积分
9.1 A Limit of Riemann Sum(Left, Right and Midpoint)黎曼和的极
9.2 The First Fundamental Theorem of Calculus微积分**基础理论
9.3 The Second Fundamental Theorem of Calculus微积分第二基础理论
9.4 Improper Integrals反常积分(广义积分)
(Practice Problems?课后练习)
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
10.3 Volume体积
10.4 Length of a Curve曲线长度
10.5 Accumulated Change累积变化
(Practice Problems?课后练习)
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
(Practice Problems?课后练习)
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
(Practice Problems?课后练习)
Chapter 13 Graphing Calculator图形计算器使用指南
13.1 TI-Nspire CX CAS面板介绍
13.2 TI-Nspire CX CAS页面的操作
13.3 TI-Nspire CX CAS针对AP微积分考试的计算内容
13.4 应用图形计算器示范求解官方样题
Chapter 14 AP Calculus BC Practice Test (AP Calculus BC模考试题)
Chapter 15 Answers参考答案
15.1 课后习题参考答案
15.2 AP Calculus BC模考试题参考答案
附录
1.AP Calculus AB&BC公式大全
2.AP Calculus BC考试中常见的极坐标图像