微積分甲(一)
Calculus (I)
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC109（光復） 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SC109（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
本課程將分成兩部分:第一部分為微分學,涵蓋極限、連續、導數等概念;第二部分則為積分學,涵蓋定積分與不定積分以及許多積分理論與技巧。 本學期用書為James Stewart寫的Calculus (Early Transcendentals)第八版。本學期的課程範圍將著重於第一章至第八章與第十章(詳細章節內容請見每週進度表)。
高中數學
無備註
以傳統式板書教學為主,視情況以投影片輔助。 助教 林承樸 email: tab314159@gmail.com Office hour: 星期三 18:30~19:20 (節次I) 地點:SA036 楊慕理 email: yml43016@gmail.com Office hour: 星期一 13:20-14:10 (節次E) 地點:SA133
微積分會考 30% 期中考 30% 小考 40% (每周考,取其中分數較高的10次) 習題請見http://calculus.nctu.edu.tw/archa/riki.php?id=8E&CID=3 或是e3教學平台
Functions and Models
1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms
- 講授：
- 4
Limits and Derivatives
2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function
- 講授：
- 8
Differentiation Rules
3.1 Derivatives of Polynomials and Exponential Functions 3.2 The Product and Quotient Rules 3.3 Derivatives of Trigonometric Functions 3.4 The Chain Rule 3.5 Implicit Differentiation 3.6 Derivatives of Logarithmic Functions ◆3.7 Rates of Change in the Natural and Social Sciences ◆3.8 Exponential Growth and Decay 3.9 Related Rates 3.10 Linear Approximations and Differentials ◆3.11 Hyperbolic Functions
- 講授：
- 8
Applications of Differentiation
4.1 Maximum and Minimum Values 4.2 The Mean Value Theorem 4.3 How Derivatives Affect the Shape of a Graph 4.4 Indeterminate Forms and L’Hospital's Rule 4.5 Summary of Curve Sketching 4.7 Optimization Problems ◆4.8 Newtons Method 4.9 Antiderivatives
- 講授：
- 8
Integrals
5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule
- 講授：
- 6
Applications of Integration
6.1 Areas between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function
- 講授：
- 3
Techniques of Integration
7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 7.4 Integration of Rational Functions by Partial Fractions ◆7.5 Strategy for integration 7.7 Approximate Integration 7.8 Improper Integrals
- 講授：
- 7
Further Applications of Integration
8.1 Arc Length 8.2 Area of a Surface of Revolution ◆8.3 Applications to Physics and Engineering ◆8.4 Applications to Economics and Biology ◆8.5 Probability
- 講授：
- 3
Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves
- 講授：
- 3
| 週次 | 主題 |
|---|---|
| 第 1 週 | 課程簡介 1.3 New Functions from Old Functions 1.4 Exponential Functions 9/13中秋節 9/10 9/13 |
| 第 2 週 | 1.5: Inverse Functions and Logarithms 2.2: The Limit of a Function 2.3: Calculating Limits Using the Limit Laws 9/17 9/20 |
| 第 3 週 | 出國開會(擇日補課) 自我預習(搭配線上影片) 2.4: The Precise Definition of a Limit 2.5: Continuity 9/24 9/27 |
| 第 4 週 | 2.6: Limits at Infinity; Horizontal Asymptotes 2.7: Derivatives and Rates of Change 2.8: The Derivative as a Function 10/1 10/4 |
| 第 5 週 | 3.1: Derivatives of Polynomials and Exponential Functions 3.2: The Product and Quotient Rules 3.3: Derivatives of Trigonometric Functions 3.4: The Chain Rule 10/8 10/11 |
| 第 6 週 | 期中考 3.5: Implicit Differentiation, Derivatives of Inverse Trigonometric Functions 3.6: Derivatives of Logarithmic Functions 10/15 10/18 |
| 第 7 週 | 3.9: Related Rates 3.10: Linear Approximations and Differentials 4.1: Maximum and Minimum Values 4.2: The Mean Value Theorem 10/22 10/25 |
| 第 8 週 | 4.3: How Derivatives Affect the Shape of a Graph 4.4: Indeterminate Forms and L’Hospital’s Rule 4.5: Summary of Curve Sketching 10/29 11/1 |
| 第 9 週 | 4.7: Optimization Problems 4.9: Antiderivatives 5.1: Areas and Distances 11/5 11/8 |
| 第 10 週 | 5.2: The Definite Integral 5.3: The Fundamental Theorem of Calculus 5.4: Indefinite Integrals and the Total Change Theorem 5.5: The Substitution Rule 11/12 11/15 |
| 第 11 週 | 6.1: Areas Between Curves 6.2: Volumes 6.3: Volumes by Cylindrical Shells 6.5: Average Value of a Function 11/19 11/22 |
| 第 12 週 | 期中考 7.1: Integration by Parts 7.2: Trigonometric Integrals 11/26 11/29 |
| 第 13 週 | 7.3: Trigonometric Substitution 7.4: Integration of Rational Functions by Partial Fractions 12/3 12/6 |
| 第 14 週 | 7.7: Approximate Integration 7.8: Improper Integrals 8.1: Arc Length 12/10 12/13 |
| 第 15 週 | 8.2: Area of a Surface of Revolution 10.1: Curves Defined by Parametric Equations 10.2: Calculus with Parametric Curves 12/17 12/20 |
| 第 16 週 | 課程統整 12/24 12/27 |
| 第 17 週 | 課程統整 12/31 1/3 |
| 第 18 週 | 課程統整 微積分會考1/8 15:30 -17:20 p.m. 1/7 |
Calculus (Early Transcendentals), James Stewart, 8th Edition
- 地點
- 科一館236
- 時間
- 每周二下午1:20-3:10
- 聯絡方式
- email: changhong@math.nctu.edu.tw