實變函數論（一）
Real Analysis (I)
學期
113-1
學分
3
學分
當期課號
536700
永久課號
SCMA30008
開課單位
應用數學系
授課教師
方向
校區
光復
類別
必修
上課時間表
| 節 | 週三 | 週四 |
|---|---|---|
2 09:00–09:50 | 實變函數論（一） SA215 | |
3 10:10–11:00 | 實變函數論（一） SA215 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
概述
1. Measure Theory 2. Integration Theory 3. Differentiation and Integration 4. Maximal operators 5. Product measures and iterated integrals 6. Tonelli theorem and Fubini theorem
先修科目
Advanced Calculus
教學方式
Check instructor's website.
評分方式
Homework: 30% Quiz: 30% Two Midterm Exams: 40% (with 20% each) Extra 10% for reporting
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | 1. Riemann integration; 2A. Outer Measures on R |
| 第 2 週 | 2B. Measurable Spaces and Functions |
| 第 3 週 | 2C. Measures and Their Properties 2D. Lebesgue Measure |
| 第 4 週 | 2D. Lebesgue Measure |
| 第 5 週 | 2E. Convergence of Measurable Functions |
| 第 6 週 | 彈性內容 |
| 第 7 週 | 3A. Integration with Respect to a Measure |
| 第 8 週 | 3B. Limits of Integrals & Integrals of Limits |
| 第 9 週 | 3B. Limits of Integrals & Integrals of Limits |
| 第 10 週 | 4A. Hardy-Littlewood Maximal Functions |
| 第 11 週 | 4B. Derivatives of Integrals |
| 第 12 週 | 彈性內容 |
| 第 13 週 | 5A. Products of Measure Spaces |
| 第 14 週 | 5B. Iterated Integrals |
| 第 15 週 | 5C. Lebesgue Integration on R^n |
| 第 16 週 | 彈性內容 |
教科書
1. S. Axler: Measure, Integration & Real Analysis. 2020. Graduate Texts in Mathematics (GTM 282), Springer Press. (open access) 2. H. L. Royden and P. M. Fitzpatrick, Real Analysis (2022,5th edition)Pearson Press. 3. R. L. Wheeden and A. Zygmund. (2015, 2nd edition) Measure and Integral: An Introduction to Real Analysis, CRC Press.
Office Hours
- 地點
- SA 349
- 時間
- By appointment
- 聯絡方式
- xfang@math.nctu.edu.tw