微積分甲(一)
Calculus A (I)
| 節 | 週一 | 週四 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC204（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 微積分甲(一) SC204（光復） 2 節連堂 | |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
learning calculus systematically
高中數學
無備註
will be provided in class
微積分會考 30%
Functions and Models
◆1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms
- 講授：
- 3
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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：
- 7
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates
- 講授：
- 4
| 週次 | 主題 |
|---|---|
| 第 1 週 | Functions and Models ◆1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms 3 ◆ 為選教內容,不列入微積分會考考試範圍。 2025-09-01(一),2025-09-04(四) |
| 第 2 週 | 2.2 The Limit of a Function 2.3 Calculating Limits Using the Limit Laws 2.4 The Precise Definition of a Limit 2025-09-08(一),2025-09-11(四) |
| 第 3 週 | 2.5 Continuity 2.6 Limits at Infinity; Horizontal Asymptotes 2.7 Derivatives and Rates of Change 2.8 The Derivative as a Function 2025-09-15(一),2025-09-18(四) |
| 第 4 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 2025-09-22(一),2025-09-25(四) |
| 第 5 週 | 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 2025-09-29(一),2025-10-02(四) |
| 第 6 週 | 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 2025-10-06(一),2025-10-09(四) |
| 第 7 週 | 4.5 Summary of Curve Sketching 4.7 Optimization Problems ◆4.8 Newtons Method 4.9 Antiderivatives 2025-10-13(一),2025-10-16(四) |
| 第 8 週 | 5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus 2025-10-20(一),2025-10-23(四) |
| 第 9 週 | 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule 2025-10-27(一),2025-10-30(四) |
| 第 10 週 | 6.1 Areas Between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function 2025-11-03(一),2025-11-06(四) |
| 第 11 週 | 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution 2025-11-10(一),2025-11-13(四) |
| 第 12 週 | 7.4 Integration of Rational Functions by Partial Fractions ◆7.5 Strategy for integration ◆7.7 Approximate Integration 7.8 Improper Integrals 2025-11-17(一),2025-11-20(四) |
| 第 13 週 | 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 2025-11-24(一),2025-11-27(四) |
| 第 14 週 | 10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves 2025-12-01(一),2025-12-04(四) |
| 第 15 週 | 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates 2025-12-08(一),2025-12-11(四) |
| 第 16 週 | 彈性內容 2025-12-15(一),2025-12-18(四) |
Calculus (Early Transcendentals), James Stewart, 9th Edition
- 地點
- to be confirmed in class.
- 時間
- Wednesday. Time to be confirmed in class.
- 聯絡方式
- xfang@nycu.edu.tw