實變函數論（一）
Real Analysis (I)
| 節 | 週三 | 週四 |
|---|---|---|
2 09:00–09:50 | 實變函數論（一） SA215（光復） | |
3 10:10–11:00 | 實變函數論（一） SA215（光復） 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
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
Advanced Calculus
無備註
Check instructor's website.
Homework: 30% Quiz: 30% Two Midterm Exams: 40% (with 20% each) Extra 10% for reporting
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| 週次 | 主題 |
|---|---|
| 第 1 週 | 1. Riemann integration; 2A. Outer Measures on R 2024-09-04(三),2024-09-05(四) |
| 第 2 週 | 2B. Measurable Spaces and Functions 2024-09-11(三),2024-09-12(四) |
| 第 3 週 | 2C. Measures and Their Properties 2D. Lebesgue Measure 2024-09-18(三),2024-09-19(四) |
| 第 4 週 | 2D. Lebesgue Measure 2024-09-25(三),2024-09-26(四) |
| 第 5 週 | 2E. Convergence of Measurable Functions 2024-10-02(三),2024-10-03(四) |
| 第 6 週 | 彈性內容 2024-10-09(三),2024-10-10(四) |
| 第 7 週 | 3A. Integration with Respect to a Measure 2024-10-16(三),2024-10-17(四) |
| 第 8 週 | 3B. Limits of Integrals & Integrals of Limits 2024-10-23(三),2024-10-24(四) |
| 第 9 週 | 3B. Limits of Integrals & Integrals of Limits 2024-10-30(三),2024-10-31(四) |
| 第 10 週 | 4A. Hardy-Littlewood Maximal Functions 2024-11-06(三),2024-11-07(四) |
| 第 11 週 | 4B. Derivatives of Integrals 2024-11-13(三),2024-11-14(四) |
| 第 12 週 | 彈性內容 2024-11-20(三),2024-11-21(四) |
| 第 13 週 | 5A. Products of Measure Spaces 2024-11-27(三),2024-11-28(四) |
| 第 14 週 | 5B. Iterated Integrals 2024-12-04(三),2024-12-05(四) |
| 第 15 週 | 5C. Lebesgue Integration on R^n 2024-12-11(三),2024-12-12(四) |
| 第 16 週 | 彈性內容 2024-12-18(三),2024-12-19(四) |
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.
- 地點
- SA 349
- 時間
- By appointment
- 聯絡方式
- xfang@math.nctu.edu.tw