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Jingdong book

AP微积分基础教程

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Books Science and Nature Mathematics

Jingdong book

AP微积分基础教程

Name: AP微积分基础教程
Brand: Jingdong book
SKU: 3137000141
Price: 43.28 USD
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Content Description

《AP微积分基础教程》介绍的是微积分学的基本内容，包括微分学、积分学和无穷级数三大块内容，并且局限于一元函数的微积分学，而不涉及更复杂的多元函数的微积分学，它分为两个层次：Calculus AB与Calculus BC，它们之间是包含与被包含的关系，即BC包含AB的全部内容，并且还包括其他更高难度的内容。

Author Description

吕小康，博士，多年从事ACT、SAT、AP、GRE、GMAT等留美考试中数学类课程的教学与研究工作。他同时也是中国人大学出版社出版的《AP统计学基础教程》的作者。每年受富臣教育委托赴美参加AP官方年会及在国内举办的各类AP研讨班，近距离接触AP资深阅卷者与命题专家，参与AP课程的教学研讨与试题分析，全面吸取原汁原味的AP教学理念，准确把握最新的考试动态与应试趋势。吕老师的教学风格严谨清晰又不失轻松活泼，已帮助多名富臣学子获得各类美国考试中的数学满分成绩。但与获得高分相比，他更感兴趣的是如何激励学生领略数学这一人类理性思维结晶的无穷魅力与深远影响。

Catalogue

第一章极限与连续
1.1 基础知识
1.2 极限与连续
1.3 本章习题与答案

第二章导数与微分
2.1 导数的定义
2.2 求导法则与基本公式
2.3 高阶导数
2.4 隐函数、参数方程所定函数的导数与相关变化率
2.5 微分与反导数
2.6 本章习题与答案

第三章导数的应用
3.1 闭区间上连续函数的性质
3.2 微分中值定理
3.3 洛必达法则（BC）
3.4 函数的单调性与曲线的凹凸性
3.5 函数的极值与最值
3.6 本章习题与答案

第四章不定积分
4.1 不定积分的定义与性质
4.2 换元积分法
4.3 基本积分技巧（BC）
4.4 本章习题与答案

第五章定积分与反常积分
5.1 定积分
5.2 反常积分（BC）
5.3 本章习题与答案

第六章积分的应用
6.1 积分中值定理
6.2 定积分的几何应用
6.3 参数方程与极坐标中的积分应用（BC）
6.4 本章习题与答案

第七章微分方程
7.1 微分方程的概念与模型
7.2 斜率场与欧拉法
7.3 本章习题与答案

第八章无穷级数（BC）
8.1 无穷级数的概念和性质
8.2 无穷级数的审敛法
8.3 幂级数
8.4 泰勒级数
8.5 本章习题与答案

第九章全真模拟试题
模拟试题一：微积分AB
模拟试题一：答案与解析（AB）
模拟试题二：微积分BC
模拟试题二：答案与解析（BC）
附录一 Tl-84AP微积分操作指南
附录二初等数学基本词汇中英文对照表
附录三 AP微积分基本词汇中英对照表
附录四初等数学基本公式表
附录五基本初等函数图像
附录六 AP微积分基本公式与重要定理列表
附录七希腊字母表

Book Abstract

第一章极限与连续

第1章是前微积分（precalculus）的内容，主要是对初等函数中的函数概念、类型、性质等进行回顾，并介绍高等数学中常见的一些基础概念与符号，同时分析极限与连续的概念、存在条件与运算性质，从而为微分与积分内容的学习奠定基础.
1.1 基础知识
1.1.1 集合、映射与函数
集合（set）与映射（mapping）的概念是高中已经学过的内容.集合是具有某种特定性质的事物组成的集体，用大写字母A、B、C表示.元素是组成集合的各个事物，用小写字母a，b， c表示.映射是集合与集合间的对应关系，它是社会或自然界中错综复杂的事物间相互依赖关系的反映.例如: y是教师 x的学生，就可以说y与x对应. 这里，教师集合X=｛x1，x2｝，学生集合Y=｛y1，y2，y3｝， x称为自变量（independent variable）， y称为因变量（dependent variable）.这是一个多值对应，与一个自变量值对应的因变量值允许多于一个.但也有许多情况下x与y之间是单值对应，即与一个自变量值对应的因变量值只能有一个，如孩子与生父.

Introduction

一、微积分学的基本特征
“在一切理论成果中，未必再有什么像17世纪下半叶微积分的发明那样，被看做人类精神的最高胜利了。”这是恩格斯的一句名言，微积分的创立是数学发展过程中的里程碑，开创了传统数学向近代数学过渡的新时期，为研究变量和函数提供了重要的方法和手段，我国数学家梁宗巨教授曾称：“如果将整个数学比做一棵大树，那么初等数学是树根，名目繁多的数学分支是树枝，而树干的主要部分就是微积分，”这是以比喻形象地说明了微积分在数学领域内部的基础地位，同时，微积分在数学之外的物理、工程、生物、医学和社会科学等学科的广泛应用，也使得它成为沟通自然科学和社会科学的一座桥梁，同时也使得微积分的学习成为各个国家高等教育的重要内容之一，
总体而言，微积分是以函数为研究对象，以极限方法为基本研究方法的数学学科，“极限”的思想贯穿着整个微积分学的始终，自然界中的很多量，仅靠有限次的代数运算是确定不了的，而必须通过分析一个无限变化过程的变化趋势才能确定下来，这就产生了极限分析方法，以极限方法研究变化率问题产生了微分学；以极限方法研究微小量的积累问题产生了积分学；而牛顿一莱布尼茨公式则揭示了两者的内在联系，建立了统一的微积分学，因此，严格意义上，我们只能说牛顿和莱布尼茨发展和整合了微积分学，而不是创造了微积分学，其数学基础在他们之前就已经形成了。
……

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