微積分甲(一)
Calculus A (I)
學期
114-1
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) SA320 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SA320 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 1: 14% Midterm 2: 14% Final Exam: 22% 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; basic properties of limit; the precise definition of a limit |
| 第 3 週 | Continuity, limit at infinity; derivative and differentiability |
| 第 4 週 | Derivatives of polynomials and (natural) exponential functions; derivatives of product and quotient; derivatives of trigonometric functions; chain rule |
| 第 5 週 | Derivatives of log functions and inverse trigo functions; logarithmic differentiation; implicit differentiation; linear approximation |
| 第 6 週 | Midterm I 7/10 |
| 第 7 週 | Maximum and minimum values; Rolle's and Mean Value Theorem; Applications of MVT |
| 第 8 週 | Understanding the shape of a graph using derivatives; L' Hospital rule |
| 第 9 週 | L' Hospital rule (cont.); curve sketching; optimization problems; antiderivatives; definite Integrals |
| 第 10 週 | Fundamental theorem of calculus; indefinite integrals; integration by substitution and integration by parts |
| 第 11 週 | Midterm II 11/11; integration by parts (cont.); trigonometric integrals |
| 第 12 週 | Trigonometric integrals (cont.); 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 | Average of value of a function; arc length and surface area; parametric curves and their calculus |
| 第 15 週 | Worked examples from previous joint exams; Final exam 12/12 |
| 第 16 週 | Joint exam 17/12 |
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