微積分甲(一)
Calculus A (I)
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC152（光復） 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SC152（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
微積分是分析學的基礎,在各科學領域有許多廣泛的應用。課程的第一部分為微分學,我們先從研究"函數"開始,介紹函數極限、連續性、導數等概念,透過這些概念將有許多應用,例如我們可以描繪複雜的函數圖形、我們可以將實際問題轉化成最佳化問題,用微分理論來解決等。第二部分則為積分學,從面積的逼近談起,引入定積分,進而學習積分理論、技巧與應用。
高中數學
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20% 小考(預計考8-10次,取最高7次成績總和,上限為20分) 50% 期中考兩次(各25%) 30% 期末會考(全校統一考試)
Functions and Models
1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms
- 講授：
- 3
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：
- 7
Integrals
5.1 The Areas and Distance Problems 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 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates
- 講授：
- 4
| 週次 | 主題 |
|---|---|
| 第 1 週 | 2025-09-02(二),2025-09-05(五) |
| 第 2 週 | 2025-09-09(二),2025-09-12(五) |
| 第 3 週 | 2025-09-16(二),2025-09-19(五) |
| 第 4 週 | 2025-09-23(二),2025-09-26(五) |
| 第 5 週 | 2025-09-30(二),2025-10-03(五) |
| 第 6 週 | 2025-10-07(二),2025-10-10(五) |
| 第 7 週 | 2025-10-14(二),2025-10-17(五) |
| 第 8 週 | 2025-10-21(二),2025-10-24(五) |
| 第 9 週 | 2025-10-28(二),2025-10-31(五) |
| 第 10 週 | 2025-11-04(二),2025-11-07(五) |
| 第 11 週 | 2025-11-11(二),2025-11-14(五) |
| 第 12 週 | 2025-11-18(二),2025-11-21(五) |
| 第 13 週 | 2025-11-25(二),2025-11-28(五) |
| 第 14 週 | 2025-12-02(二),2025-12-05(五) |
| 第 15 週 | 2025-12-09(二),2025-12-12(五) |
| 第 16 週 | 2025-12-16(二),2025-12-19(五) |
Calculus (Early Transcendentals), James Stewart, 9th Edition
- 地點
- 科一館SA236
- 時間
- Office hours: 周一下午: 200-3:00 或是email預約時間(建議)
- 聯絡方式
- changhong@math.nctu.edu.tw