微積分甲(一)
Calculus A (I)
學期
113-1
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
王賜聖
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
先修科目
高中數學
教學方式
其餘補充事項,會在第一次上課時與修課同學們說明清楚。
評分方式
(1) 小考和作業佔學期總成績30%。 (2) 第一次期中考佔學期總成績 20%,第二次期中考佔學期總成績20%,考試範圍與時間將另行公佈。 (3) 陽明交通大學期末微積分會考,成績佔學期總成績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 | Chapter 0. Preliminaries Chapter 1. Limits and Derivative -Limits of Functions -The Precise Definition of a Limit |
| 第 2 週 | Chapter 1. Limits and Derivative -Calculating Limits Using the Limit Laws -Infinite Limits; Vertical Asymptotes -Continuity |
| 第 3 週 | Chapter 1. Limits and Derivative -Continuity -Limits at infinity/Asymptoes -Tangents -Derivatives |
| 第 4 週 | Chapter 2. Differentiation Rules -Derivatives of Polynomials -The Product and Quotient Rules -The Chain Rule -Derivatives of Exponential Functions -Derivatives of Trigonometric Functions |
| 第 5 週 | Chapter 2. Differentiation Rules -Implicit Differentiation -Derivatives of Inverse Trigonometric Functions -Derivatives of Logarithmic Functions |
| 第 6 週 | Midterm Exam |
| 第 7 週 | Chapter 2. Differentiation Rules -Derivatives of Inverse Functions -Linear Approximations/Newton's Method -Differentials Chapter 3. Applications of Differentiation -Maximum and Minimum Values -Closed Interval Method |
| 第 8 週 | Chapter 3. Applications of Differentiation -The First Derivative Test -The Second Derivative Test and Concavity -Summary of Curve Sketching |
| 第 9 週 | Chapter 3. Applications of Differentiation -Mean Value Theorem -Proof of Increasing/Decreasing Test -Proof of Concavity Test |
| 第 10 週 | Chapter 3. Applications of Differentiation -Indeterminate Forms and l'Hospital's Rule -Antiderivative Chapter 4. Indefinite Integrals & Techniques of Integration -Indefinite Integrals -The Substitution Rule |
| 第 11 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Integration by Parts -Trigonometric Integrals -Trigonometric Substitution |
| 第 12 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Trigonometric Substitution -Integration of Rational Functions by Partial Fractions -Half-Angle Substitution |
| 第 13 週 | Midterm Exam Chapter 5 Integrals - Area Below a Positive Graph |
| 第 14 週 | Chapter 5 Integrals - Definite Integral - The Fundamental Theorem of Calculus - Improper Integrals (Type 1) |
| 第 15 週 | Chapter 5 Integrals - Improper Integrals (Type 2) - A Comparison Test for Improper Integrals Chapter 6 Applications of Integration - Area of a Region Between Two Curves - Volumes (using Cross-Sections) - Volumes (by Cylindrical Shells) - Arc Length - Area of a Surface of Revolution - Curves Defined by Parametric Equations - Calculus with Parametric Curves |
| 第 16 週 | Review 2024-12-18(三) The Spring Semester of Calculus Final Exam in 2024 |
教科書
Calculus (Early Transcendentals), James Stewart, 9th Edition
Office Hours
- 聯絡方式
- 老師的e-mail: sswangtw@math.nctu.edu.tw