微積分甲(一)
Calculus A (I)
學期
113-1
學分
4
學分
當期課號
564001
永久課號
GECS10001
開課單位
微積分教學小組
授課教師
阮志豪
校區
光復
類別
必修
上課時間表
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC106 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SC106 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
先修科目
高中數學
教學方式
Use e3 system.
評分方式
Quizzes: 20% Midterm: 25% Final Exam: 25% Joint Exam:30%
課程大綱
- Functions and Models
- Limits and Derivatives
- Differentiation Rules
- Applications of Differentiation
- Integrals
- Applications of Integration
- Techniques of Integration
- Further Applications of Integration
- Parametric Equations and Polar Coordinates
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Exponential functions; inverse functions and logarithms |
| 第 2 週 | The limit of a function, calculating limits using the limit laws; the precise definition of a limit; basic continuity |
| 第 3 週 | Continuity; limits at infinity, horizontal asymptotes |
| 第 4 週 | Derivative and differentiability; derivatives of polynomials and (natural) exponential functions, derivatives of sum, difference, product, and quotient |
| 第 5 週 | Derivatives of trigonometric functions; chain rule; implicit differentiation; derivatives of logarithmic functions |
| 第 6 週 | Logarithmic differentiation, derivatives of inverse trigonometric functions; linear approximation and differentials; maximum and minimum values; Rolle's Theorem and Mean Value Theorem |
| 第 7 週 | Applications of MVT; understanding the shape of a graph using derivatives; L' Hospital rule |
| 第 8 週 | Midterm 25/10 |
| 第 9 週 | Curve sketching, optimization problems |
| 第 10 週 | Optimization (cont.); antiderivatives; definite Integrals and the fundamental theorem of calculus |
| 第 11 週 | Indefinite integrals; integration by substitution; integration by parts |
| 第 12 週 | Trigonometric integrals; trigonometric substitution; integration of rational functions by partial fractions |
| 第 13 週 | Improper Integrals; areas between curves; volumes and volumes by cylindrical shells |
| 第 14 週 | Volumes by cylindrical shells (cont.); average of value of a function; arc length and surface area; parametric curves and their calculus |
| 第 15 週 | Parametric curves and their calculus (cont.); worked examples from previous joint exams. Final exam 13/12 |
| 第 16 週 | Joint exam 18/12 |
教科書
Calculus (Early Transcendentals), James Stewart, 9th Edition
Office Hours
- 地點
- SA 341
- 時間
- Send an e-mail to me to make appointment.
- 聯絡方式
- chyuen@math.nctu.edu.tw