微積分甲(一)
Calculus A (I)
學期
114-1
學分
4
學分
當期課號
564018
永久課號
GECS10001
開課單位
微積分教學小組
授課教師
方向
校區
光復
類別
必修
上課時間表
| 節 | 週一 | 週四 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC204 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 微積分甲(一) SC204 2 節連堂 | |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
概述
learning calculus systematically
先修科目
高中數學
教學方式
will be provided in class
評分方式
微積分會考 30%
課程大綱
- Functions and Models
- Limits and Derivatives
- Differentiation Rules
- Applications of Differentiation
- Integrals
- Applications of Integration
- Techniques of Integration
- Further Applications of Integration
- Parametric Equations and Polar Coordinates
週次計畫
| 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。 |
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| 第 7 週 | 4.5 Summary of Curve Sketching 4.7 Optimization Problems ◆4.8 Newtons Method 4.9 Antiderivatives |
| 第 8 週 | 5.1 Areas and Distances 5.2 The Definite Integral 5.3 The Fundamental Theorem of Calculus |
| 第 9 週 | 5.4 Indefinite Integrals and the Net Change Theorem 5.5 The Substitution Rule |
| 第 10 週 | 6.1 Areas Between Curves 6.2 Volumes 6.3 Volumes by Cylindrical Shells 6.5 Average Value of a Function |
| 第 11 週 | 7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution |
| 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 |
| 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 |
| 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 16 週 | 彈性內容 |
教科書
Calculus (Early Transcendentals), James Stewart, 9th Edition
Office Hours
- 地點
- to be confirmed in class.
- 時間
- Wednesday. Time to be confirmed in class.
- 聯絡方式
- xfang@nycu.edu.tw