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
教師未提供此項資料
高中數學
無備註
其餘補充事項,會在第一次上課時與修課同學們說明清楚。
(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%。
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 10.3 Polar Coordinates 10.4 Areas in Polar Coordinates
- 講授：
- 4
| 週次 | 主題 |
|---|---|
| 第 1 週 | Chapter 0. Preliminaries Chapter 1. Limits and Derivative -Limits of Functions -The Precise Definition of a Limit 2024-09-02(一),2024-09-05(四) |
| 第 2 週 | Chapter 1. Limits and Derivative -Calculating Limits Using the Limit Laws -Infinite Limits; Vertical Asymptotes -Continuity 2024-09-09(一),2024-09-12(四) |
| 第 3 週 | Chapter 1. Limits and Derivative -Continuity -Limits at infinity/Asymptoes -Tangents -Derivatives 2024-09-16(一),2024-09-19(四) |
| 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 2024-09-23(一),2024-09-26(四) |
| 第 5 週 | Chapter 2. Differentiation Rules -Implicit Differentiation -Derivatives of Inverse Trigonometric Functions -Derivatives of Logarithmic Functions 2024-09-30(一),2024-10-03(四) |
| 第 6 週 | Midterm Exam 2024-10-07(一),2024-10-10(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 2024-10-14(一),2024-10-17(四) |
| 第 8 週 | Chapter 3. Applications of Differentiation -The First Derivative Test -The Second Derivative Test and Concavity -Summary of Curve Sketching 2024-10-21(一),2024-10-24(四) |
| 第 9 週 | Chapter 3. Applications of Differentiation -Mean Value Theorem -Proof of Increasing/Decreasing Test -Proof of Concavity Test 2024-10-28(一),2024-10-31(四) |
| 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 2024-11-04(一),2024-11-07(四) |
| 第 11 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Integration by Parts -Trigonometric Integrals -Trigonometric Substitution 2024-11-11(一),2024-11-14(四) |
| 第 12 週 | Chapter 4. Indefinite Integrals & Techniques of Integration -Trigonometric Substitution -Integration of Rational Functions by Partial Fractions -Half-Angle Substitution 2024-11-18(一),2024-11-21(四) |
| 第 13 週 | Midterm Exam Chapter 5 Integrals - Area Below a Positive Graph 2024-11-25(一),2024-11-28(四) |
| 第 14 週 | Chapter 5 Integrals - Definite Integral - The Fundamental Theorem of Calculus - Improper Integrals (Type 1) 2024-12-02(一),2024-12-05(四) |
| 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 2024-12-09(一),2024-12-12(四) |
| 第 16 週 | Review 2024-12-18(三) The Spring Semester of Calculus Final Exam in 2024 2024-12-16(一),2024-12-19(四) |
Calculus (Early Transcendentals), James Stewart, 9th Edition
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- 老師的e-mail: sswangtw@math.nctu.edu.tw