This is a beta course, so its structure, chapters, and examples may continue to change.
Differential Calculus of One Variable
Differential Calculus
Course Highlights
- Build intuition for derivatives as both limits of average rates and slopes of tangents.
- Use linear approximation to turn hard nonlinear problems into easy local estimates.
- Locate extrema and understand how monotonicity, concavity, and inflection points interact.
- Connect theory with practice: optimization, error estimation, and modeling show up throughout.
Great math is learned twice: first roughly, then precisely. Skim once for the big picture, then revisit for the proofs and details.
Summary
本文出现的符号
| 符号 | 类型 | 读音/说明 | 在本文中的含义 |
|---|---|---|---|
| 数学符号 | “f prime of x” | 函数在点 处的导数（切线斜率） | |
| 数学符号 | Delta x（德尔塔） | 自变量的变化量，用于平均变化率 |
中英对照
| 中文术语 | 英文术语 | 音标 | 说明 |
|---|---|---|---|
| 一元函数 | single-variable function | /ˈsɪŋɡl̩ ˈvɛərɪəbl ˈfʌŋkʃən/ | 只含一个自变量的函数 |
| 微分学 | differential calculus | /ˌdɪfəˈrɛnʃəl ˈkælkjələs/ | 研究导数与微分的数学分支 |
| 导数 | derivative | /dɪˈrɪvətɪv/ | 变化率或切线斜率的度量 |
| 线性近似 | linear approximation | /ˈlɪniə əˌprɒksɪˈmeɪʃən/ | 用切线替代原函数的局部估计 |
| 极值 | extremum | /ɪkˈstriːməm/ | 函数的极大值或极小值 |