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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復閤函數 2.4 Parametric Functions參變量函數 2.5 Polar Functions極坐標函數 2.6 Vector Functions嚮量函數 2.7 Transforming of Functions函數變換 【Practice Problems·課後練習】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：找漸近綫 3.6 Continuity連續 【Practice Problems·課後練習】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可導與連續的關係 【Practice Problems·課後練習】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嚮量函數求導 【Practice Problems·課後練習】Chapter 6 Applications of Derivatives導數應用 6.1 Equations of Tangent Lines and Normal Lines切綫和法綫方程 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 【Practice Problems·課後練習】Chapter 7 Differentials微分 7.1 Defi n ition of Differential微分定義 7.2 Linear Approximation綫性估算 7 3 Euler’S Method歐拉法則 【Practice Problems·課後練習】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 【Practice Problems·課後練習】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） 【Practice Problems·課後練習】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麵積 10.3 Volume體積 10.4 Length of a Curve麯綫長度 【Practice Problems·課後練習】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 【Practice Problems·課後練習】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 【Practice Problems·課後練習】Answers
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