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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