calculus
Core Sentence / 核心句
Calculus studies change, accumulation, and limits.
中文理解：微积分研究变化、累积和极限，是 AP Calculus 和 Physics C 的共同语言。
Formula / 公式或规则
Course/language hub card.
When To Use / 什么时候用
作为低层入口连接 derivative、integral、series。
Watch Out / 易错点
这个页是索引，不是某个定理。
Search and Source Mentions / 搜索与出现位置
Mentioned In / 出现位置
- AP电磁学第2次正课-连续带电体电场与电通量 · Why We Need Calculus
Why We Need Calculus
- 01 - The Essence of Calculus · 1. Calculus is about turning hard problems into sums of tiny pieces.
1. Calculus is about turning hard problems into sums of tiny pieces.
- 01 - The Essence of Calculus · 3Blue1Brown - The Essence of Calculus 01
3Blue1Brown - The Essence of Calculus 01
- 02 - The Paradox of the Derivative · 3Blue1Brown - The Essence of Calculus 02 - The Paradox of the Derivative
3Blue1Brown - The Essence of Calculus 02 - The Paradox of the Derivative
- 03 - Derivative Formulas through Geometry · 3Blue1Brown - The Essence of Calculus 03 - Derivative Formulas through Geometry
3Blue1Brown - The Essence of Calculus 03 - Derivative Formulas through Geometry
- 微积分BC第13次正课-无穷级数判敛 · Knowledge Point 5: Integral Test
这个方法的底层直觉来自 01 - The Essence of Calculus 里的“many tiny rectangles become area under a graph”。在 AP 题里，Integral Test 把级数的尾部行为转成 improper integral 来判断。
- 微积分BC第13次正课-无穷级数判敛 · Knowledge Point A: Polar Slope Means $dy/dx$
在 calculus 里就是问：
- 微积分BC第13次正课-无穷级数判敛 · Knowledge Point E: Polar Area Formula
这个和 01 - The Essence of Calculus 的主线相连：很多 tiny pieces accumulate into total area。