微積分甲(一)
Calculus A (I)
| 節 | 週二 | 週五 |
|---|---|---|
3 10:10–11:00 | 微積分甲(一) SC106（光復） 2 節連堂 | |
4 11:10–12:00 | ||
5 13:20–14:10 | 微積分甲(一) SC106（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: 25% Final Exam: 25% 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 ◆10.3 Polar Coordinates ◆10.4 Calculus in Polar Coordinates
- 講授：
- 2
| 週次 | 主題 |
|---|---|
| 第 1 週 | Exponential functions; inverse functions and logarithms 2024-09-03(二),2024-09-06(五) |
| 第 2 週 | The limit of a function, calculating limits using the limit laws; the precise definition of a limit; basic continuity 2024-09-10(二),2024-09-13(五) |
| 第 3 週 | Continuity; limits at infinity, horizontal asymptotes 2024-09-17(二),2024-09-20(五) |
| 第 4 週 | Derivative and differentiability; derivatives of polynomials and (natural) exponential functions, derivatives of sum, difference, product, and quotient 2024-09-24(二),2024-09-27(五) |
| 第 5 週 | Derivatives of trigonometric functions; chain rule; implicit differentiation; derivatives of logarithmic functions 2024-10-01(二),2024-10-04(五) |
| 第 6 週 | Logarithmic differentiation, derivatives of inverse trigonometric functions; linear approximation and differentials; maximum and minimum values; Rolle's Theorem and Mean Value Theorem 2024-10-08(二),2024-10-11(五) |
| 第 7 週 | Applications of MVT; understanding the shape of a graph using derivatives; L' Hospital rule 2024-10-15(二),2024-10-18(五) |
| 第 8 週 | Midterm 25/10 2024-10-22(二),2024-10-25(五) |
| 第 9 週 | Curve sketching, optimization problems 2024-10-29(二),2024-11-01(五) |
| 第 10 週 | Optimization (cont.); antiderivatives; definite Integrals and the fundamental theorem of calculus 2024-11-05(二),2024-11-08(五) |
| 第 11 週 | Indefinite integrals; integration by substitution; integration by parts 2024-11-12(二),2024-11-15(五) |
| 第 12 週 | Trigonometric integrals; trigonometric substitution; integration of rational functions by partial fractions 2024-11-19(二),2024-11-22(五) |
| 第 13 週 | Improper Integrals; areas between curves; volumes and volumes by cylindrical shells 2024-11-26(二),2024-11-29(五) |
| 第 14 週 | Volumes by cylindrical shells (cont.); average of value of a function; arc length and surface area; parametric curves and their calculus 2024-12-03(二),2024-12-06(五) |
| 第 15 週 | Parametric curves and their calculus (cont.); worked examples from previous joint exams. Final exam 13/12 2024-12-10(二),2024-12-13(五) |
| 第 16 週 | Joint exam 18/12 2024-12-17(二),2024-12-20(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