微積分甲(一)
Calculus (I)
| 節 | 週一 | 週四 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC206（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 微積分甲(一) SC206（光復） 2 節連堂 | |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
微積分是分析學的基礎,在各領域有許多廣泛的應用。一般而言,課程可以將分成兩部分,第一部分為微分學,涵蓋函數極限、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。
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(未定)
微積分期末會考 30% 期中考(兩次各15%)合計30% 小考 40% (每周考,取其中分數較高的10次)
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 |
| 第 2 週 | 1.5: Inverse Functions and Logarithms 2.2: The Limit of a Function 2.3: Calculating Limits Using the Limit Laws |
| 第 3 週 | 2.4: The Precise Definition of a Limit 2.5: Continuity |
| 第 4 週 | 2.6: Limits at Infinity; Horizontal Asymptotes 2.7: Derivatives and Rates of Change 2.8: The Derivative as a Function |
| 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 |
| 第 6 週 | 3.5: Implicit Differentiation, Derivatives of Inverse Trigonometric Functions 3.6: Derivatives of Logarithmic Functions 3.9: Related Rates |
| 第 7 週 | 3.10: Linear Approximations and Differentials 4.1: Maximum and Minimum Values 4.2: The Mean Value Theorem 第一次期中考 |
| 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 |
| 第 9 週 | 4.7: Optimization Problems 4.9: Antiderivatives 5.1: Areas and Distances |
| 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 |
| 第 11 週 | 6.1: Areas Between Curves 6.2: Volumes 6.3: Volumes by Cylindrical Shells 6.5: Average Value of a Function |
| 第 12 週 | 7.1: Integration by Parts 7.2: Trigonometric Integrals |
| 第 13 週 | 7.3: Trigonometric Substitution 7.4: Integration of Rational Functions by Partial Fractions 第二次期中考 |
| 第 14 週 | 7.7: Approximate Integration 7.8: Improper Integrals 8.1: Arc Length |
| 第 15 週 | 8.2: Area of a Surface of Revolution 10.1: Curves Defined by Parametric Equations 10.2: Calculus with Parametric Curves |
| 第 16 週 | 課程統整 |
| 第 17 週 | 課程統整 |
| 第 18 週 | 課程統整 |
Calculus (Early Transcendentals), James Stewart, 8e版本
- 地點
- 科一館236
- 時間
- 每周五上午10:10-11:50 or by appointment
- 聯絡方式
- email: changhong@math.nctu.edu.tw