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
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,透過這些概念我們有許多應用,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
無備註
以傳統式板書教學為主,視情況以投影片、線上影片輔助。
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次成績總和上限為30分)
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 |
| 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 |
Calculus (Early Transcendentals), James Stewart, 9e版本
- 地點
- 科一館236
- 時間
- 每周一上午10:10-11:50 or by appointment (建議)
- 聯絡方式
- email: changhong@math.nctu.edu.tw