微積分甲(一)
Calculus (I)
學期
110-1
學分
4
學分
當期課號
0318
永久課號
DAM1367
開課單位
微積分教學小組
授課教師
吳昌鴻
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) SC206 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SC206 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
概述
微積分是分析學的基礎,在各領域有許多廣泛的應用。課程的第一部分為微分學,涵蓋函數極限、連續性、導數等概念;第二部分則為積分學,涵蓋由面積的逼近引入定積分,進而學習積分理論與技巧。透過這兩部份的概念進而能有一些不同領域的應用。
先修科目
高中數學
教學方式
以傳統式板書教學為主,視情況以投影片、線上影片輔助。
評分方式
微積分期末會考 30% 期中考(兩次各20%)合計40% 小考 30% (整學期會考10-12次左右,取其中分數較高的8次成績總和)
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 | 課程簡介 1.3 New Functions from Old Functions 1.4 Exponential Functions |
| 第 2 週 | 1.5: Inverse Functions and Logarithms 2.2: The Limit of a Function |
| 第 3 週 | 2.3: Calculating Limits Using the Limit Laws 2.4: The Precise Definition of a Limit |
| 第 4 週 | 2.5: Continuity 2.6: Limits at Infinity; Horizontal Asymptotes 2.7: Derivatives and Rates of Change |
| 第 5 週 | 2.8: The Derivative as a Function 3.1: Derivatives of Polynomials and Exponential Functions 3.2: The Product and Quotient Rules |
| 第 6 週 | 3.3: Derivatives of Trigonometric Functions 3.4: The Chain Rule 3.5: Implicit Differentiation, Derivatives of Inverse Trigonometric Functions |
| 第 7 週 | 3.6: Derivatives of Logarithmic Functions 3.10: Linear Approximations and Differentials 4.1: Maximum and Minimum Values |
| 第 8 週 | 4.2: The Mean Value Theorem 4.3: How Derivatives Affect the Shape of a Graph 第一次期中考 |
| 第 9 週 | 4.4: Indeterminate Forms and L'Hospital Rule 4.5: Summary of Curve Sketching 4.9: Antiderivatives |
| 第 10 週 | 5.1: Areas and Distances 5.2: The Definite Integral 5.3: The Fundamental Theorem of Calculus |
| 第 11 週 | 5.4: Indefinite Integrals and the Total Change Theorem 5.5: The Substitution Rule 6.1: Areas Between Curves 6.2: Volumes |
| 第 12 週 | 6.3: Volumes by Cylindrical Shells 6.5: Average Value of a Function 7.1: Integration by Parts 7.2: Trigonometric Integrals 7.3: Trigonometric Substitution |
| 第 13 週 | 7.4: Integration of Rational Functions by Partial Fractions 7.8: Improper Integrals 8.1: Arc Length 8.2: Area of a Surface of Revolution |
| 第 14 週 | 10.1: Curves Defined by Parametric Equations 10.2: Calculus with Parametric Curves |
| 第 15 週 | 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates 第二次期中考 |
| 第 16 週 | 課程統整 微積分會考 |
| 第 17 週 | 彈性授課 |
| 第 18 週 | 彈性授課 |
教科書
Calculus (Early Transcendentals), James Stewart, 9e版本
Office Hours
- 地點
- 科一館236
- 時間
- 每周一上午10:10-11:50 or by appointment
- 聯絡方式
- email: changhong@math.nctu.edu.tw