第1章 AP微積分簡介 Introduction of AP Calculus 1.1 課程及考試The Courses and Examinations 1.2 AP微積分AB和BC大綱要求 The Examination Outline of AP Calculus AB & BC 1.3 AP微積分參考辭彙表 Reference Vocabulary of AP Calculus 1.4 圖形計算器的使用 Use of Graphing Calculators 第2章 函數 Functions 2.1 函數的定義 Definition of Functions 2.2 函數的基本性質 Function Basic Properties 2.3 基本初等函數 Basic Elementary Functions 2.4 反函數&複合函數 Inverse Functions & Composite Functions 2.5 函數變換 Transforming of Functions 2.6 #參數方程&向量函數 Parametric Equations & Vector Functions 2.7 #極坐標函數 Polar Functions 2.8 習題 Practice Exercises 第3章 極限 Limit 3.1 極限的定義 Definition of the Limit 3.2 極限存在的判定 The Limit does Exist or Not 3.3 極限的運算 Operations of Limit 3.4 極限的應用 Applications of Limit 3.5 習題 Practice Exercises 第4章 連續 Continuity 4.1 連續性的定義 Definition of the Continuity 4.2 間斷點的分類 Kinds of Discontinuities 4.3 連續函數定理 The Continuous Functions Theorem 4.4 習題 Practice Exercises 第5章 導數和微分 Derivative and Differential 5.1 導數的定義 Definition of the Derivative 5.2 可導性和連續性 Derivability and Continuity 5.3 導數的基本公式和法則 Basic Differentiation Formulas and Rules 5.4 鏈式法則和反函數求導 The Chain Rule & Derivative of an Inverse Function 5.5 隱函數求導和二階導數 Implicit Differentiation & Second Derivatives 5.6 #參數方程求導 Derivatives of Parametric Equations 5.7 #向量函數和極坐標函數求導 Derivatives of Vector Functions and Polar Functions 5.8 微分 Differential 5.9 習題 Practice Exercises 第6章 微分的應用 Applications of Differential Calculus 6.1 切線方程和法線方程Equations of Tangent and Normal 6.2 最值問題The Problems of Maxima and Minima 6.3 運動問題The Problems of Motion 6.4 微分中值定理The Mean Value Theorem for Derivatives 6.5 洛必達法則L』Hpital』s Rule 6.6 估算問題The Problems of Estimate 6.7 #歐拉方法Euler』s Method 6.8 習題Practice Exercises 第7章 不定積分 The Indefinite Integral 7.1 不定積分的定義Definition of The Indefinite Integral 7.2 不定積分公式Formulas of The Indefinite Integral 7.3 U-替換法U-Substitution 7.4 #分部積分法Integration by Parts 7.5 #有理函數的積分Integration of Rational Functions
7.6 不定積分的應用Applications of Indefinite Integral 7.7 習題Practice Exercises 第8章 定積分 The Definite Integral 8.1 黎曼和與梯形法則Riemann Sums and Trapezoid Rule 8.2 定積分的定義Definition of the Definite Integral 8.3 微積分基本定理The Fundamental Theorem of Calculus 8.4 定積分的性質Properties of Definite Integral 8.5 積分中值定理The Mean Value Theorem for Integrals 8.6 定積分的計算The Operations of Definite Integrate 8.7 #廣義積分Improper Integrals 8.8 習題Practice Exercises 第9章 積分的應用 Applications of Integral 9.1 面積Area 9.2 體積Volume 9.3 #弧長 Arc Length 9.4 位移和距離Displacement and Distance 9.5 習題 Practice Exercises 第10章 微分方程 Differential Equations 10.1 一階微分方程First-Order Differential Equations 10.2 求解可分離變數微分方程Solving Separable D 10.3 斜率場 Slope Fields 10.4 指數增長與衰減 Exponential Growth and Decay 10.5 約束增長與衰減 Restricted Growth and Decay 10.6 #邏輯斯諦微分方程Logistic Differential Equation 10.7 習題 Practice Exercises 第11章 無窮級數 Infinite Series 11.1 數列的極限 The Limit of The Sequence 11.2 無窮級數 Infinite Series 11.3 四類重要級數Four Important Series 11.4 正項級數的四大判別法Four Tests of Nonnegative Series 11.5 絕對收斂和條件收斂 Absolute and Conditional Convergence 11.6 冪級數 Power Series 11.7 泰勒級數和麥克勞林級數 Taylor and Maclaurin Series 11.8 冪級數的計算 Computations with Power Series 11.9 習題 Practice Exercises 習題答案Practice Answer 附錄Appendix A.1 常用公式和定理Common Formulas and Theorems A.2 AP微積分公式總結Summary AP Calculus Formula A.3 VIP服務及網站 參考文獻References
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