作者：（美）William Ma,（美）Carolyn Wheater 编著
页数：489
出版社：西安交通大学出版社
出版日期：2013
ISBN：9787560552484
电子书格式：pdf/epub/txt
内容简介
本系列ap考试丛书引进自美国知名教育出版公司mcgraw-hill
education，由ap考试相关领域专家编写，是美国本土大学课堂使用教材，可以帮助考生提前适应全英学习模式。此系列中，ap各学科分册紧扣考试命题特点，以“五步”方案为学习框架，囊括与考试相关的学科要点。同时，还精选针对性练习以及全真模拟试题，配以准确答案和详尽解析，利于考生巩固所学，紧抓重点，取得高分。
作者简介
William Ma，教授微积分多年；曾获得哥伦比亚大学学士和硕士学位；后又曾担任何瑞克斯学区的数学部主席，直至退休。
Carolyn Wheater，毕业于马萨诸塞大学和玛丽蒙特曼哈顿大学，教授数学近30年；现在南丁格尔班福德学校担任初高中部数学老师。
本书特色
科学的“五步”学习方案
巧妙的解题方法和策略
详细的学科内容讲解
典型的针对性练习
高仿真模拟套题
目录
step 1 set up your study plan
1 what you need to know about the ap calculus ab/bc exams
1.1 what is covered on the ap calculus exams?
1.2 what is the format of the ap calculus ap/bc exams?
1.3 what are the advanced placement exam grades?
how is the ap calculus exam grade calculated?
1.4 which graphing calculators are allowed for the exam?
calculators and other devices not allowed for the ap calculusexam
other restrictions on calculators
2 how to plan your time
2.1 three approaches to preparing for the ap calculus exam
overview of the three plans
2.2 calendar for each plan
summary of the three study plans
step 2 determine your test readiness
3 take a diagnostic exam
3.1 getting started!
3.2 diagnostic test
3.3 answers to diagnostic test
3.4 solutions to diagnostic test
3.5 calculate your score
short-answer questions
ap calculus ab/bc diagnostic exam
step 3 develop strategies for success
4 how to approach each question type
4.1 the multiple-choice questions
4.2 the free-response questions
4.3 using a graphing calculator
4.4 taking the exam
what do i need to bring to the exam?
tips for taking the exam
step 4 review the knowledge you need to score high
5 limits and continuity
5.1 the limit of a function
definition and properties of limits
evaluating limits
one-sided limits
squeeze theorem
5.2 limits involving infinities
infinite limits (as x → a)
limits at infinity (as x → ±∞)
horizontal and vertical asymptotes
5.3 continuity of a function
continuity of a function at a number
continuity of a function over an interval
theorems on continuity
5.4 rapid review
5.5 practice problems
5.6 cumulative review problems
5.7 solutions to practice problems
5.8 solutions to cumulative review problems
6 differentiation
6.1 derivatives of algebraic functions
definition of the derivative of a function
power rule
the sum, difference, product, and quotient rules
the chain rule
6.2 derivatives of trigonometric, inverse trigonometric,
exponential, and logarithmic functions
derivatives of trigonometric functions
derivatives of inverse trigonometric functions
derivatives of exponential and logarithmic functions
6.3 implicit differentiation
procedure for implicit differentiation
6.4 approximating a derivative
6.5 derivatives of inverse functions
6.6 higher order derivatives
6.7 indeterminate forms
l’h?opital’s rule for indeterminate forms 97
6.8 rapid review
6.9 practice problems
6.10 cumulative review problems
6.11 solutions to practice problems
6.12 solutions to cumulative review problems
7 graphs of functions and derivatives
7.1 rolle’s theorem, mean value theorem, and extreme valuetheorem
rolle’s theorem
mean value theorem
extreme value theorem
7.2 determining the behavior of functions
test for increasing and decreasing functions
first derivative test and second derivative test for relativeextrema
test for concavity and points of inflection
7.3 sketching the graphs of functions
graphing without calculators
graphing with calculators
7.4 graphs of derivatives
7.5 parametric, polar, and vector representations
parametric curves 130
polar equations
types of polar graphs
symmetry of polar graphs
vectors
vector arithmetic
7.6 rapid review
7.7 practice problems
7.8 cumulative review problems
7.9 solutions to practice problems
7.10 solutions to cumulative review problems
8 applications of derivatives
8.1 related rate
general procedure for solving related rate problems
common related rate problems
inverted cone (water tank) problem
shadow problem
angle of elevation problem
8.2 applied maximum and minimum problems
general procedure for solving applied maximum and minim
