第1章AP微积分简介 Introduction of AP Calculus001
1．1课程及考试The Courses and Examinations001
1．2AP微积分AB和BC大纲要求 The Examination Outline of AP Calculus AB & BC004
1．3AP微积分参考词汇表 Reference Vocabulary of AP Calculus006
1．4图形计算器的使用 Use of Graphing Calculators013
第2章函数 Functions019
2．1函数的定义 Definition of Functions020
2．2函数的基本性质 Function Basic Properties022
2．3基本初等函数 Basic Elementary Functions023
2．4反函数&复合函数 Inverse Functions & Composite Functions033
2．5函数变换 Transforming of Functions035
2．6#参数方程&向量函数 Parametric Equations & Vector Functions037
2．7#极坐标函数 Polar Functions039
2．8习题 Practice Exercises041
第3章极限 Limit043
3．1极限的定义 Definition of the Limit044
3．2极限存在的判定 The Limit does Exist or Not045
3．3极限的运算 Operations of Limit047
3．4极限的应用 Applications of Limit052
3．5习题 Practice Exercises053
第4章连续 Continuity055
4．1连续性的定义 Definition of the Continuity056
4．2间断点的分类 Kinds of Discontinuities059
4．3连续函数定理 The Continuous Functions Theorem061
4．4习题 Practice Exercises063
第5章导数和微分 Derivative and Differential065
5．1导数的定义 Definition of the Derivative066
5．2可导性和连续性 Derivability and Continuity072
5．3导数的基本公式和法则 Basic Differentiation Formulas and Rules075
5．4链式法则和反函数求导 The Chain Rule & Derivative of an Inverse Function077
5．5隐函数求导和二阶导数 Implicit Differentiation & Second Derivatives082
5．6#参数方程求导 Derivatives of Parametric Equations088
5．7#向量函数和极坐标函数求导 Derivatives of Vector Functions and Polar Functions090
5．8微分 Differential093
5．9习题 Practice Exercises096
第6章微分的应用 Applications of Differential Calculus098
6．1切线方程和法线方程Equations of Tangent and Normal099
6．2最值问题The Problems of Maxima and Minima101
6．3运动问题The Problems of Motion112
6．4微分中值定理The Mean Value Theorem for Derivatives118
6．5洛必达法则L’Hpital’s Rule120
6．6估算问题The Problems of Estimate125
6．7#欧拉方法Euler’s Method129
6．8习题Practice Exercises130
第7章不定积分 The Indefinite Integral132
7．1不定积分的定义Definition of The Indefinite Integral133
7．2不定积分公式Formulas of The Indefinite Integral135
7．3U-替换法U-Substitution138
7．4#分部积分法Integration by Parts148
7．5#有理函数的积分Integration of Rational Functions153
7．6不定积分的应用Applications of Indefinite Integral156
7．7习题Practice Exercises157
第8章定积分 The Definite Integral159
8．1黎曼和与梯形法则Riemann Sums and Trapezoid Rule160
8．2定积分的定义Definition of the Definite Integral165
8．3微积分基本定理The Fundamental Theorem of Calculus169
8．4定积分的性质Properties of Definite Integral174
8．5积分中值定理The Mean Value Theorem for Integrals176
8．6定积分的计算The Operations of Definite Integrate178
8．7#广义积分Improper Integrals180
8．8习题Practice Exercises185
第9章积分的应用 Applications of Integral186
9．1面积Area187
9．2体积Volume195
9．3#弧长 Arc Length204
9．4位移和距离Displacement and Distance206
9．5习题 Practice Exercises207
第10章微分方程 Differential Equations209
10．1一阶微分方程First-Order Differential Equations210
10．2求解可分离变量微分方程Solving Separable D．E．211
10．3斜率场 Slope Fields213
10．4指数增长与衰减 Exponential Growth and Decay216
10．5约束增长与衰减 Restricted Growth and Decay219
10．6#逻辑斯谛微分方程Logistic Differential Equation222
10．7习题 Practice Exercises225
第11章无穷级数 Infinite Series226
11．1数列的极限 The Limit of The Sequence227
11．2无穷级数 Infinite Series228
11．3四类重要级数Four Important Series232
11．4正项级数的四大判别法Four Tests of Nonnegative Series235
11．5绝对收敛和条件收敛 Absolute and Conditional Convergence240
11．6幂级数 Power Series242
11．7泰勒级数和麦克劳林级数 Taylor and Maclaurin Series245
11．8幂级数的计算 Computations with Power Series251
11．9习题 Practice Exercises254
习题答案Practice Answer255
附录Appendix287
A．1常用公式和定理Common Formulas and Theorems287
A．2AP微积分公式总结Summary AP Calculus Formula291
A．3VIP服务及网站298
参考文献References299
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