微積分甲(一)
Calculus A (I)
學期
114-1
學分
4
學分
當期課號
564012
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) SC106 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 微積分甲(一) SC106 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
Additional information will be explained to students during the first class meeting.
評分方式
(1) Quizzes and homework will account for 30% of the final grade. Weekly homework will be announced after class on Thursdays. Assignments should be submitted as PDF files via the E3 system. Late homework will not be accepted! If a quiz is given, it will be held on a Monday, with at least one week's prior notice. (2) The first midterm exam will account for 20%, and the second midterm exam will account for 20% of the final grade. The exam schedule and coverage will be announced in class. (3) The NYCU Calculus Final Examination will account for 30% of the final grade.
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 Derivatives -Limits of Functions -The Precise Definition of a Limit |
| 第 2 週 | Chapter 1. Limits and Derivatives -Calculating Limits Using the Limit Laws -Infinite Limits; Vertical Asymptotes -Continuity |
| 第 3 週 | Chapter 1. Limits and Derivatives -Continuity -Limits at infinity/Asymptotes -Tangents -Derivatives |
| 第 4 週 | Chapter 1. Limits and Derivatives -Derivatives Chapter 2. Differentiation Rules -Derivatives of Polynomials -The Product and Quotient Rules -The Chain Rule |
| 第 5 週 | 09-29: Make-up holiday as Teachers' Day (holiday) Chapter 2. Differentiation Rules -Derivatives of Exponential Functions -Derivatives of Trigonometric Functions -Implicit Differentiation |
| 第 6 週 | 10-06: The Mid-Autumn Festival (holiday) Chapter 2. Differentiation Rules -Implicit Differentiation -Derivatives of Inverse Trigonometric Functions -Derivatives of Logarithmic Functions |
| 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 | Midterm Exam Chapter 3. Applications of Differentiation -The First Derivative Test -The Second Derivative Test and Concavity |
| 第 9 週 | Chapter 3. Applications of Differentiation -Summary of Curve Sketching -Mean Value Theorem -Proof of Increasing/Decreasing Test -Proof of Concavity Test -Indeterminate Forms and l'Hospital's Rule (1) |
| 第 10 週 | Chapter 3. Applications of Differentiation -Indeterminate Forms and l'Hospital's Rule (2) -Antiderivative Chapter 4. Indefinite Integrals & Techniques of Integration -Indefinite Integrals -The Substitution Rule -Integration by Parts |
| 第 11 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Trigonometric Integrals -Trigonometric Substitution -Integration of Rational Functions by Partial Fractions (1) |
| 第 12 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Integration of Rational Functions by Partial Fractions (2) -Half-Angle Substitution Chapter 5 Integrals - Area Below a Positive Graph (1) |
| 第 13 週 | Midterm Exam Chapter 5 Integrals - Area Below a Positive Graph (2) - Definite Integral (1) |
| 第 14 週 | Chapter 5 Integrals - Definite Integral (2) - The Fundamental Theorem of Calculus - Improper Integrals - A Comparison Test for Improper Integrals |
| 第 15 週 | Chapter 6 Applications of Integration - Area of a Region Between Two Curves - Volumes (using Cross-Sections) - Volumes of Solids of Revolution (by Disk method, Washer method) - Volumes (by Shells method) - Arc Length - Area of a Surface of Revolution - Curves Defined by Parametric Equations - Calculus with Parametric Curves |
| 第 16 週 | Review 2025-12-17 (Wed) The Spring Semester of Calculus Final Exam in 2025 |
教科書
Calculus (Early Transcendentals), James Stewart, 9th Edition
Office Hours
- 地點
- SA238
- 聯絡方式
- e-mail:sswangtw@nycu.edu.tw