AP微積分

Chapter 1 Introduction of AP Calculus Exam AP微積分考試介紹
Chapter 2 Functions函數
2.1 Five Basic Elementary Functions五種基本初等函數
2.2 Inverse Functions反函數
2.3 Composite Functions復合函數
2.4 Parametric Functions參變量函數
2.5 Polar Functions極坐標函數
2.6 Vector Functions向量函數
2.7 Transforming of Functions函數變換
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Chapter 3 Limit and Continuity極限與連續
3.1 Definition of a Limit極限的定義
3.2 Limit Laws極限（存在）定理
3.3 Rules of Limits極限的運算法則
3.4 Two Important Limits兩個重要極限
3.5 Application of Limits：Finding Asymptotes極限的應用：找漸近線
3.6 Continuity連續
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Chapter 4 Definition of Derivative導數定義
4.1 Definition of Derivative導數的定義
4-2 ORe—Sided Derivative單側導數
4.3 The Geometric Interpretation of Derivative導數的幾何意義
4.4 The Relation Between Differentiability and Continuity可導與連續的關系
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Chapter 5 Rules for Finding Derivatives求導法則
5.1 Basic Rules for Finding Derivatives導數基本運算
5.2 High Order Derivatives高階導數
5.3 Implicit Differentiation「隱函數」求導
5.4 The Derivative of an Inverse Function反函數求導
5.5 Derivatives of Parametric Functions參數方程求導
5.6 Derivatives of Polar Functions極坐標函數求導
5.7 Derivatives of Vector Functions向量函數求導
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Chapter 6 Applications of Derivatives導數應用
6.1 Equations of Tangent Lines and Normal Lines切線和法線方程
6.2 The Mean Value Theorem for Derivatives微分中值定理
6.3 Related Rates相關變化率
6.4 Motion運動學
6.5 Maxima and Minima最大值和最小值
6.6 L』Hopital』S Rule洛比達法則
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Chapter 7 Differentials微分
7.1 Defi n ition of Differential微分定義
7.2 Linear Approximation線性估算
7 3 Euler』S Method歐拉法則
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Chapter 8 The Indefinite Integral不定積分
8.1 The Antiderivative原函數
812 Integration Formulas積分公式
8.3 U—Substitution換元法、
8.4 Integ ration by Parts分部積分
8.5 The Method of Partial Fractions分式拆分求積分
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Chapter 9 The Definite Integral定積分
9.1 A Limit of Riemann Sum（Left，Right and Midpoint）黎曼和的極限
9.2 The Fi rst Fundamental Theorem of Calculus微積分第一基礎理論
9.3 The Second Fundamental Theorem of Calculus微積分第二基礎理論
9.4 Improper Integrals反常積分（廣義積分）
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Chapter 10 Applications of Integral積分應用
10.1 The Mean Value Theorem for Integ rals積分中值定理
10.2 Area面積
10.3 Volume體積
10.4 Length of a Curve曲線長度
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Chapter 11 Differential Equations微分方程
11.1 Separation Variables可分離變量的微分方程
11.2 Logistic Differential Equation邏輯斯蒂微分方程
11.3 Slope Fields（Direction Fields）斜率場
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Chapter 1 2 Infinite Series無窮級數
12.1 ORe Definition for Infinite Series一個定義
12.2 Two Limits兩個極限
12.3 Three Tests of Series三大審斂法
12.4 Four Important Series四種重要級數
12.5 Five Formulas of Power Series and Taylor Series五個重要公式
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