微積分甲(一)
Calculus A (I)
| 節 | 週一 | 週四 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC106（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 微積分甲(一) SC106（光復） 2 節連堂 | |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
教師未提供此項資料
高中數學
無備註
Additional information will be explained to students during the first class meeting.
(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.
Functions and Models
◆1.3 New Functions from Old Functions 1.4 Exponential Functions 1.5 Inverse Functions and Logarithms
- 講授：
- 3
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
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
備註：◆ 為選教內容,不列入微積分會考考試範圍。
Parametric Equations and Polar Coordinates
10.1 Curves Defined by Parametric Equations 10.2 Calculus with Parametric Curves
- 講授：
- 4
| 週次 | 主題 |
|---|---|
| 第 1 週 | Chapter 0. Preliminaries Chapter 1. Limits and Derivatives -Limits of Functions -The Precise Definition of a Limit 2025-09-01(一),2025-09-04(四) |
| 第 2 週 | Chapter 1. Limits and Derivatives -Calculating Limits Using the Limit Laws -Infinite Limits; Vertical Asymptotes -Continuity 2025-09-08(一),2025-09-11(四) |
| 第 3 週 | Chapter 1. Limits and Derivatives -Continuity -Limits at infinity/Asymptotes -Tangents -Derivatives 2025-09-15(一),2025-09-18(四) |
| 第 4 週 | Chapter 1. Limits and Derivatives -Derivatives Chapter 2. Differentiation Rules -Derivatives of Polynomials -The Product and Quotient Rules -The Chain Rule 2025-09-22(一),2025-09-25(四) |
| 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 2025-09-29(一),2025-10-02(四) |
| 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 2025-10-06(一),2025-10-09(四) |
| 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 2025-10-13(一),2025-10-16(四) |
| 第 8 週 | Midterm Exam Chapter 3. Applications of Differentiation -The First Derivative Test -The Second Derivative Test and Concavity 2025-10-20(一),2025-10-23(四) |
| 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) 2025-10-27(一),2025-10-30(四) |
| 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 2025-11-03(一),2025-11-06(四) |
| 第 11 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Trigonometric Integrals -Trigonometric Substitution -Integration of Rational Functions by Partial Fractions (1) 2025-11-10(一),2025-11-13(四) |
| 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) 2025-11-17(一),2025-11-20(四) |
| 第 13 週 | Midterm Exam Chapter 5 Integrals - Area Below a Positive Graph (2) - Definite Integral (1) 2025-11-24(一),2025-11-27(四) |
| 第 14 週 | Chapter 5 Integrals - Definite Integral (2) - The Fundamental Theorem of Calculus - Improper Integrals - A Comparison Test for Improper Integrals 2025-12-01(一),2025-12-04(四) |
| 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 2025-12-08(一),2025-12-11(四) |
| 第 16 週 | Review 2025-12-17 (Wed) The Spring Semester of Calculus Final Exam in 2025 2025-12-15(一),2025-12-18(四) |
Calculus (Early Transcendentals), James Stewart, 9th Edition
- 地點
- SA238
- 時間
- 教師未提供此項資料
- 聯絡方式
- e-mail:sswangtw@nycu.edu.tw