AP微積分

Chapter 1 Introduction of AP Calculus Exam AP微積分考試介紹
Chapter 2 Functions函數(shù)
　2.1 Five Basic Elementary Functions五種基本初等函數(shù)
　2.2 Inverse Functions反函數(shù)
　2.3 Composite Functions復(fù)合函數(shù)
　2.4 Parametric Functions參變量函數(shù)
　2.5 Polar Functions極坐標(biāo)函數(shù)
　2.6 Vector Functions向量函數(shù)
　2.7 Transforming of Functions函數(shù)變?
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Chapter 3 Limit and Continuity極限與連續(xù)
　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(yùn)算法則
　3.4 Two Important Limits兩個(gè)重要極限
　3.5 Application of Limits: Finding Asymptotes極限的應(yīng)用：找漸近線
　3.6 Continuity連續(xù)
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Chapter 4 Definition of Derivative導(dǎo)數(shù)定義
　4.1 Definition of Derivative導(dǎo)數(shù)的定義
　4.2 One-Sided Derivative單側(cè)導(dǎo)數(shù)
　4.3 The Geometric Interpretation of Derivative導(dǎo)數(shù)的幾何意義
　4.4 The Relation Between Differentiability and Continuity可導(dǎo)與連續(xù)的關(guān)系
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Chapter 5 Rules for Finding Derivatives求導(dǎo)法則
　5.1 Basic Rules for Finding Derivatives導(dǎo)數(shù)基本運(yùn)算
　5.2 High Order Derivatives高階導(dǎo)數(shù)
　5.3 Implicit Differentiation“隱函數(shù)”求導(dǎo)
　5.4 The Derivative of an Inverse Function?函數(shù)求導(dǎo)
　5.5 Derivatives of Parametric Functions參數(shù)方程求導(dǎo)
　5.6 Derivatives of Polar Functions極坐標(biāo)函數(shù)求導(dǎo)
　5.7 Derivatives of Vector Functions向量函數(shù)求導(dǎo)
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Chapter 6 Applications of Derivatives導(dǎo)數(shù)應(yīng)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(guān)變化率
　6.4 Motion運(yùn)動(dòng)學(xué)
　6.5 Maxima and Minima最大值和最小值
　6.6 L’Hopital’s Rule洛比達(dá)法則
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Chapter 7 Differentials微分
　7.1 Definition 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(shù)
　8.2 Integration Formulas積分公式
　8.3 U-Substitution換元法
　8.4 Integration 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 First Fundamental Theorem of Calculus微積分第一基礎(chǔ)理論
　9.3 The Second Fundamental Theorem of Calculus微積分第二基礎(chǔ)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(yīng)用
　10.1 The Mean Value Theorem for Integrals 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 12 Infinite Series無窮級數(shù)
　12.1 One Definition for Infinite Series一個(gè)定義
　12.2 Two Limits兩個(gè)極限
　12.3 Three Tests of Series三大審斂法
　12.4 Four Important Series四種重要級數(shù)
　12.5 Five Formulas of Power Series and Taylor Series五個(gè)重要公式
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