微积分（英文版·第八版）

　　The art of teaching， Mark Van Doren said， is the art of assisting discovery. I have tried to write a book that assists students in discovering calculus-both for its practical power and its surprising beauty. In this edition， as in the first seven editions， I aim to convey to the student a sense of the utility of calculus and develop technical competence， but I also strive to give some appreciation for the intrinsic beauty of the subject. Newton undoubtedly experienced a sense of triumph when he made his great discoveries. I want students to share some of that excitement.The emphasis is on understanding concepts. I think that nearly everybody agrees that this should be the primary goal of calculus instruction. In fact， the impetus for the current calculus reform movement came from the Tulane Conference in 1986， which formulated as their first recommendation：Focus on conceptual understanding.I have tried to implement this goal through the Rule of Three： Topics should be presented geometrically， numerically， and algebraically. Visualization， numerical and graphical experimentation， and other approaches have changed how we teach conceptual reasoning in fundamental ways. More recently， the Rule of Three has been expanded to become the Rule of Four by emphasizing the verbal， or descriptive， point of view as well.In writing the eighth edition my premise has been that it is possible to achieve conceptual understanding and still retain the best traditions of traditional calculus. The book contains elements of reform. but within the context of a traditional curriculum.

暂缺《微积分（英文版·第八版）》作者简介

前言
学生须知
计算器、计算机以及其他图形设备
诊断性测试
微积分概述
第1章 函数和极限
1．1 函数表示的四种方法
1．2 函数变换
1．3 函数极限
1．4 利用极限运算法则求极限
1．5 极限的严格定义
1．6 连续性
复习
求解题目的一些原则
第2章 导数
2．1 导数与变化率
2．2 函数的导数
2．3 微分公式
2．4 三角函数的导数
2．5 链式法则
2．6 隐函数的导数
复习
第3章 微分的应用
3．1 最大值和最小值
3．2 中值定理
3．3 导数值对函数形状的影响
3．4 无穷大时的极限值；水平渐近线
3．5 函数作图概述
3．6 原函数
复习
第4章 积分
4．1 面积和距离
4．2 定积分
探索项目·面积函数
4．3 微积分基本定理
4．4 不定积分和牛顿-莱布尼茨公式
4．5 换元积分法
复习
第5章 定积分的应用
5．1 曲线间的面积
5．2 体积
5．3 旋转体的体积
5．4 功
5．5 函数的积分平均值
复习
第6章 反函数
6．1 反函数
6．2 指数函数及其导数
6．3 对数函数
6．4 对数函数的导数
6．5 指数增长与指数衰减
6．6 未定式与洛必达法则
复习
……
第7章 积分的方法
第8章 积分的进一步应用
第9章 微分方程
第10章 参数方程和极坐标
第11章 偏导数
第12章 多重积分