AP Calculus

CB 考纲
AP®︎ Calculus BC | Khan Academy (半被墙)

进行一个 calculus 的自学。记一些需要花点心思的东西（

Unit 9 各种东西

Parametric Equations (参数方程)

TOPIC 9.1 Defining and Differentiating Parametric Equations
TOPIC 9.2 Second Derivatives of Parametric Equations

同济高数上 P104 - 107

曲线积分

TOPIC 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
TOPIC 9.7 Defining Polar Coordinates and Differentiating in Polar Form
TOPIC 9.8 Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

同济高数上 P274 - 286

TOPIC 9.9 Finding the Area of the Region Bounded by Two Polar Curves

Finding Area Bounded By Two Polar Curves - YouTube

Unit 10 无穷级数

定义与审敛法

TOPIC 10.1 Defining Convergent and Divergent Infinite Series
TOPIC 10.2 Working with Geometric Series
TOPIC 10.3 The nth Term Test for Divergence
TOPIC 10.6 Comparison Tests for Convergence
TOPIC 10.7 Alternating Series Test for Convergence
TOPIC 10.8 Ratio Test for Convergence
TOPIC 10.9 Determining Absolute or Conditional Convergence

同济高数下 P251 - 267，性质 12345，定理 123478，只需掌握定理内容与基础应用，直接去搜章节标题其实就可以了。记熟。

TOPIC 10.5 Harmonic Series and p-Series
TOPIC 10.4 Integral Test for Convergence

Khan Academy。或者什么别的地方，反正比较 trivial。

• Integral Test: 若 单调减，则 收敛的充要条件是 为有限值，即其可以判 convergency 也可以判 divergency。
• Ratio Test: converge absolutely, diverge, inconclusive
• 可积性：无界一定不可积 / 不连续不一定不可积
• conditionally convergent: convergent but not absolutely convergent
• Euler's Method
• point of inflection:
• 常用函数的麦克劳林展开 | xiangwei's blog
• Calculus AP Vocabulary List.docx
• critical point: 导数为 0 或不存在
• concave up 是下凸（。。
• asymptote: 渐近线
• ap calculus 不给公示表。。