Chapter 1 Introduction of AP Calculus Exam AP微積分考試介紹 1
Chapter 2 Functions函數 5
2.1 Five Basic Elementary Functions五種基本初等函數 6
2.2 Inverse Functions反函數 16
2.3 Composite Functions復合函數 16
2.4 Parametric Functions參變量函數 17
2.5 Polar Functions極坐標函數 17
2.6 Vector Functions向量函數 20
2.7 Transforming of Functions函數變換 21
【Practice Problems•課後練習】 22
Chapter 3 Limit and Continuity極限與連續 26
3.1 Definition of a Limit極限的定義 26
3.2 Limit Laws極限(存在)定理 27
3.3 Rules of Limits極限的運算法則 30
3.4 Two Important Limits兩個重要極限 33
3.5 Application of Limits: Finding Asymptotes極限的應用:找漸近線 34
3.6 Continuity連續 35
【Practice Problems•課後練習】 39
Chapter 4 Definition of Derivative導數定義 44
4.1 Definition of Derivative導數的定義 44
4.2 One-Sided Derivative單側導數 49
4.3 The Geometric Interpretation of Derivative導數的幾何意義 49
4.4 The Relation Between Differentiability and Continuity可導與連續的關繫 50
【Practice Problems•課後練習】 52
Chapter 5 Rules for Finding Derivatives求導法則 56
5.1 Basic Rules for Finding Derivatives導數基本運算 57
5.2 High Order Derivatives高階導數 62
5.3 Implicit Differentiation“隱函數”求導 63
5.4 The Derivative of an Inverse Function反函數求導 67
5.5 Derivatives of Parametric Functions參數方程求導 69
5.6 Derivatives of Polar Functions極坐標函數求導 71
5.7 Derivatives of Vector Functions向量函數求導 72
【Practice Problems•課後練習】 74
Chapter 6 Applications of Derivatives導數應用 79
6.1 Equations of Tangent Lines and Normal Lines切線和法線方程 81
6.2 The Mean Value Theorem for Derivatives微分中值定理 82
6.3 Related Rates相關變化率 83
6.4 Motion運動學 86
6.5 Maxima and Minima值和小值 89
6.6 L’Hopital’s Rule洛比達法則 95
【Practice Problems•課後練習】 97
Chapter 7 Differentials微分 101
7.1 Definition of Differential微分定義 101
7.2 Linear Approximation 線性估算 104
7.3 Euler’s Method歐拉法則 105
【Practice Problems•課後練習】 108
Chapter 8 The Indefinite Integral不定積分 112
8.1 The Antiderivative原函數 112
8.2 Integration Formulas積分公式 114
8.3 U-Substituti法 116
8.4 Integration by Parts分部積分 119
8.5 The Method of Partial Fractions分式拆分求積分 122
【Practice Problems•課後練習】 124
Chapter 9 The Definite Integral定積分 128
9.1 A Limit of Riemann Sum(Left, Right and Midpoint)黎曼和的極限 128
9.2 The First Fundamental Theorem of Calculus微積分基礎理論 132
9.3 The Second Fundamental Theorem of Calculus微積分第二基礎理論 134
9.4 Improper Integrals反常積分(廣義積分) 137
【Practice Problems•課後練習】 140
Chapter 10 Applications of Integral積分應用 145
10.1 The Mean Value Theorem for Integrals 積分中值定理 145
10.2 Area面積 146
10.3 Volume體積 151
10.4 Length of a Curve曲線長度 158
10.5 Accumulated Change累積變化 159
【Practice Problems•課後練習】 160
Chapter 11 Differential Equations微分方程 164
11.1 Separation Variables可分離變量的微分方程 164
11.2 Logistic Differential Equation邏輯斯蒂微分方程 166
11.3 Slope Fields (Direction Fields)斜率場 169
【Practice Problems•課後練習】 173
Chapter 12 Infinite Series無窮級數 177
12.1 One Definition for Infinite Series一個定義 178
12.2 Two Limits兩個極限 179
12.3 Three Tests of Series三大審斂法 180
12.4 Four Important Series四種重要級數 182
12.5 Five Formulas of Power Series and Taylor Series五個重要公式 187
【Practice Problems•課後練習】 195
Chapter 13 Graphing Calculator圖形計算器使用指南 197
13.1 TI-Nspire CX CAS面板介紹 197
13.2 TI-Nspire CX CAS頁面的操作 204
13.3 TI-Nspire CX CAS針對AP微積分考試的計算內容 226
13.4 應用圖形計算器示範求解官方樣題 231
Chapter 14 AP Calculus BC Practice Test (AP Calculus BC模考試題) 238
Chapter 15 Answers參考答案 265
15.1 課後習題參考答案 265
15.2 AP Calculus BC模考試題參考答案 289
附 錄 308
- AP Calculus AB&BC公式大全 308
2. AP Calculus BC考試中常見的極坐標圖像 314