微積分甲(一)
Calculus A (I)
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SA320（光復） 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SA320（光復） 2 節連堂 | |
6 14:20–15:10 |
* 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
Use e3 system.
Quizzes: 20% Midterm 1: 14% Midterm 2: 14% Final Exam: 22% Joint Exam: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：◆ indicates optional material and is not included in the syllabus of joint exam, the same below (選教內容,不列入微積分會考考試範圍,下同)
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
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
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
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
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 | Exponential functions; inverse functions and logarithms 2025-09-02(二),2025-09-05(五) |
| 第 2 週 | The limit of a function; basic properties of limit; the precise definition of a limit 2025-09-09(二),2025-09-12(五) |
| 第 3 週 | Continuity, limit at infinity; derivative and differentiability 2025-09-16(二),2025-09-19(五) |
| 第 4 週 | Derivatives of polynomials and (natural) exponential functions; derivatives of product and quotient; derivatives of trigonometric functions; chain rule 2025-09-23(二),2025-09-26(五) |
| 第 5 週 | Derivatives of log functions and inverse trigo functions; logarithmic differentiation; implicit differentiation; linear approximation 2025-09-30(二),2025-10-03(五) |
| 第 6 週 | Midterm I 7/10 2025-10-07(二),2025-10-10(五) |
| 第 7 週 | Maximum and minimum values; Rolle's and Mean Value Theorem; Applications of MVT 2025-10-14(二),2025-10-17(五) |
| 第 8 週 | Understanding the shape of a graph using derivatives; L' Hospital rule 2025-10-21(二),2025-10-24(五) |
| 第 9 週 | L' Hospital rule (cont.); curve sketching; optimization problems; antiderivatives; definite Integrals 2025-10-28(二),2025-10-31(五) |
| 第 10 週 | Fundamental theorem of calculus; indefinite integrals; integration by substitution and integration by parts 2025-11-04(二),2025-11-07(五) |
| 第 11 週 | Midterm II 11/11; integration by parts (cont.); trigonometric integrals 2025-11-11(二),2025-11-14(五) |
| 第 12 週 | Trigonometric integrals (cont.); trigonometric substitution; integration of rational functions by partial fractions 2025-11-18(二),2025-11-21(五) |
| 第 13 週 | Improper Integrals; areas between curves; volumes and volumes by cylindrical shells 2025-11-25(二),2025-11-28(五) |
| 第 14 週 | Average of value of a function; arc length and surface area; parametric curves and their calculus 2025-12-02(二),2025-12-05(五) |
| 第 15 週 | Worked examples from previous joint exams; Final exam 12/12 2025-12-09(二),2025-12-12(五) |
| 第 16 週 | Joint exam 17/12 2025-12-16(二),2025-12-19(五) |
Calculus (Early Transcendentals), James Stewart, 9th Edition
- 地點
- SA 341
- 時間
- Send an e-mail to me to make appointment.
- 聯絡方式
- chyuen@math.nctu.edu.tw