Chapter 3 Limit and Continuity极限与连续 26
3.1 Definition of a Limit极限的定义 26
3.2 Limit Laws极限（存在）定理 27
3.3 Rules of Limits极限的运算法则 30
3.4 Two Important Limits两个重要极限 33
3.5 Application of Limits： Finding Asymptotes极限的应用：找渐近线 34
3.6 Continuity连续 35
【Practice Problems课后练习】 39
Chapter 4 Definition of Derivative导数定义 44
4.1 Definition of Derivative导数的定义 44
4.2 One-Sided Derivative单侧导数 49
4.3 The Geometric Interpretation of Derivative导数的几何意义 49
4.4 The Relation Between Differentiability and Continuity可导与连续的关系 50
【Practice Problems课后练习】 52
Chapter 5 Rules for Finding Derivatives求导法则 56
5.1 Basic Rules for Finding Derivatives导数基本运算 57
5.2 High Order Derivatives高阶导数 62
5.3 Implicit Differentiation隐函数求导 63
5.4 The Derivative of an Inverse Function反函数求导 67
5.5 Derivatives of Parametric Functions参数方程求导 69
5.6 Derivatives of Polar Functions极坐标函数求导 71
5.7 Derivatives of Vector Functions向量函数求导 72
【Practice Problems课后练习】 74
Chapter 6 Applications of Derivatives导数应用 79
6.1 Equations of Tangent Lines and Normal Lines切线和法线方程 81
6.2 The Mean Value Theorem for Derivatives微分中值定理 82
6.3 Related Rates相关变化率 83
6.4 Motion运动学 86
6.5 Maxima and Minima最大值和最小值 89
6.6 LHopitals Rule洛比达法则 95
【Practice Problems课后练习】 97
Chapter 8 The Indefinite Integral不定积分 112
8.1 The Antiderivative原函数 112
8.2 Integration Formulas积分公式 114
8.3 U-Substitution换元法 116
8.4 Integration by Parts分部积分 119
8.5 The Method of Partial Fractions分式拆分求积分 122
【Practice Problems课后练习】 124
Chapter 9 The Definite Integral定积分 128
9.1 A Limit of Riemann SumLeft, Right and Midpoint黎曼和的极限 128
9.2 The First Fundamental Theorem of Calculus微积分第一基础理论 132
9.3 The Second Fundamental Theorem of Calculus微积分第二基础理论 134
9.4 Improper Integrals反常积分（广义积分） 137
【Practice Problems课后练习】 140
Chapter 10 Applications of Integral积分应用 145
10.1 The Mean Value Theorem for Integrals 积分中值定理 145
10.2 Area面积 146
10.3 Volume体积 151
10.4 Length of a Curve曲线长度 158
10.5 Accumulated Change累积变化 159
【Practice Problems课后练习】 160
Chapter 12 Infinite Series无穷级数 177
12.1 One Definition for Infinite Series一个定义 178
12.2 Two Limits两个极限 179
12.3 Three Tests of Series三大审敛法 180
12.4 Four Important Series四种重要级数 182
12.5 Five Formulas of Power Series and Taylor Series五个重要公式 187
【Practice Problems课后练习】 195
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