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Chapter 1 Introduction of AP Calculus Exam AP΢»ý·Ö¿¼ÊÔ½éÉÜ 1 Chapter 2 Functionsº¯Êý 5 2.1 Five Basic Elementary FunctionsÎåÖÖ»ù±¾³õµÈº¯Êý 6 2.2 Inverse Functions·´º¯Êý 16 2.3 Composite Functions¸´ºÏº¯Êý 16 2.4 Parametric Functions²Î±äÁ¿º¯Êý 17 2.5 Polar Functions¼«×ø±êº¯Êý 17 2.6 Vector FunctionsÏòÁ¿º¯Êý 20 2.7 Transforming of Functionsº¯Êý±ä»» 21 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 22 Chapter 3 Limit and Continuity¼«ÏÞÓëÁ¬Ðø 26 3.1 Definition of a Limit¼«Ï޵Ķ¨Òå 26 3.2 Limit Laws¼«ÏÞ(´æÔÚ)¶¨Àí 27 3.3 Rules of Limits¼«ÏÞµÄÔËËã·¨Ôò 30 3.4 Two Important LimitsÁ½¸öÖØÒª¼«ÏÞ 33 3.5 Application of Limits: Finding Asymptotes¼«ÏÞµÄÓ¦ÓãºÕÒ½¥½üÏß 34 3.6 ContinuityÁ¬Ðø 35 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 39 Chapter 4 Definition of Derivativeµ¼Êý¶¨Òå 44 4.1 Definition of Derivativeµ¼ÊýµÄ¶¨Òå 44 4.2 One-Sided Derivativeµ¥²àµ¼Êý 49 4.3 The Geometric Interpretation of Derivativeµ¼ÊýµÄ¼¸ºÎÒâÒå 49 4.4 The Relation Between Differentiability and Continuity¿Éµ¼ÓëÁ¬ÐøµÄ¹Øϵ 50 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 52 Chapter 5 Rules for Finding DerivativesÇóµ¼·¨Ôò 56 5.1 Basic Rules for Finding Derivativesµ¼Êý»ù±¾ÔËËã 57 5.2 High Order Derivatives¸ß½×µ¼Êý 62 5.3 Implicit Differentiation¡°Òþº¯Êý¡±Çóµ¼ 63 5.4 The Derivative of an Inverse Function·´º¯ÊýÇóµ¼ 67 5.5 Derivatives of Parametric Functions²ÎÊý·½³ÌÇóµ¼ 69 5.6 Derivatives of Polar Functions¼«×ø±êº¯ÊýÇóµ¼ 71 5.7 Derivatives of Vector FunctionsÏòÁ¿º¯ÊýÇóµ¼ 72 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 74 Chapter 6 Applications of Derivativesµ¼ÊýÓ¦Óà 79 6.1 Equations of Tangent Lines and Normal LinesÇÐÏߺͷ¨Ïß·½³Ì 81 6.2 The Mean Value Theorem for Derivatives΢·ÖÖÐÖµ¶¨Àí 82 6.3 Related RatesÏà¹Ø±ä»¯ÂÊ 83 6.4 MotionÔ˶¯Ñ§ 86 6.5 Maxima and Minima*´óÖµºÍ*Сֵ 89 6.6 L'Hopital's RuleÂå±È´ï·¨Ôò 95 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 97 Chapter 7 Differentials΢·Ö 101 7.1 Definition of Differential΢·Ö¶¨Òå 101 7.2 Linear Approximation ÏßÐÔ¹ÀËã 104 7.3 Euler's MethodÅ·À­·¨Ôò 105 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 108 Chapter 8 The Indefinite Integral²»¶¨»ý·Ö 112 8.1 The AntiderivativeÔ­º¯Êý 112 8.2 Integration Formulas»ý·Ö¹«Ê½ 114 8.3 U-Substitution»»Ôª·¨ 116 8.4 Integration by Parts·Ö²¿»ý·Ö 119 8.5 The Method of Partial Fractions·Öʽ²ð·ÖÇó»ý·Ö 122 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 124 Chapter 9 The Definite Integral¶¨»ý·Ö 128 9.1 A Limit of Riemann Sum(Left, Right and Midpoint)ÀèÂüºÍµÄ¼«ÏÞ 128 9.2 The First Fundamental Theorem of Calculus΢»ý·Ö**»ù´¡ÀíÂÛ 132 9.3 The Second Fundamental Theorem of Calculus΢»ý·ÖµÚ¶þ»ù´¡ÀíÂÛ 134 9.4 Improper Integrals·´³£»ý·Ö(¹ãÒå»ý·Ö) 137 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 140 Chapter 10 Applications of Integral»ý·ÖÓ¦Óà 145 10.1 The Mean Value Theorem for Integrals »ý·ÖÖÐÖµ¶¨Àí 145 10.2 AreaÃæ»ý 146 10.3 VolumeÌå»ý 151 10.4 Length of a CurveÇúÏß³¤¶È 158 10.5 Accumulated ChangeÀÛ»ý±ä»¯ 159 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 160 Chapter 11 Differential Equations΢·Ö·½³Ì 164 11.1 Separation Variables¿É·ÖÀë±äÁ¿µÄ΢·Ö·½³Ì 164 11.2 Logistic Differential EquationÂß¼­Ë¹µÙ΢·Ö·½³Ì 166 11.3 Slope Fields (Direction Fields)бÂʳ¡ 169 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 173 Chapter 12 Infinite SeriesÎÞÇÊý 177 12.1 One Definition for Infinite SeriesÒ»¸ö¶¨Òå 178 12.2 Two LimitsÁ½¸ö¼«ÏÞ 179 12.3 Three Tests of SeriesÈý´óÉóÁ²·¨ 180 12.4 Four Important SeriesËÄÖÖÖØÒª¼¶Êý 182 12.5 Five Formulas of Power Series and Taylor SeriesÎå¸öÖØÒª¹«Ê½ 187 ¡¾Practice Problems¡¤¿ÎºóÁ·Ï°¡¿ 195 Chapter 13 Graphing CalculatorͼÐμÆËãÆ÷ʹÓÃÖ¸ÄÏ 197 13.1 TI-Nspire CX CASÃæ°å½éÉÜ 197 13.2 TI-Nspire CX CASÒ³ÃæµÄ²Ù×÷ 204 13.3 TI-Nspire CX CASÕë¶ÔAP΢»ý·Ö¿¼ÊԵļÆËãÄÚÈÝ 226 13.4 Ó¦ÓÃͼÐμÆËãÆ÷ʾ·¶Çó½â¹Ù·½ÑùÌâ 231 Chapter 14 AP Calculus BC Practice Test (AP Calculus BCÄ£¿¼ÊÔÌâ) 238 Chapter 15 Answers²Î¿¼´ð°¸ 265 15.1 ¿ÎºóÏ°Ìâ²Î¿¼´ð°¸ 265 15.2 AP Calculus BCÄ£¿¼ÊÔÌâ²Î¿¼´ð°¸ 289 ¸½ ¼ 308 1. AP Calculus AB&BC¹«Ê½´óÈ« 308 2. AP Calculus BC¿¼ÊÔÖг£¼ûµÄ¼«×ø±êͼÏñ 314