實變函數論(一)
Real Analysis (I)
| 節 | 週二 | 週四 |
|---|---|---|
3 10:10–11:00 | 實變函數論(一) SA215（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 實變函數論(一) SA215（光復） |
* 根據陽明交大上課時間表所列
This course is designed to acquaint the graduate students in the applied mathematics department with basic ideas and tools in modern analysis. This comprises the subjects of real analysis and functional analysis, the analytic tools developed in the first half of the 20th century. We will treat real analysis mainly in the first semester and functional analysis in the second. The purpose is to lay down a solid foundation for further usage in some other theoretical or applied areas. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.
Advanced calculus, linear algebra
無備註
Wheeden, Richard L and Zygmund, Antoni , Measure and integral : an introduction to real analysis , M. Dekker, c1977.
(1) Assigned homework problems: 2/5 of the final grade, (2) Three midterm exams : 3/5 of the final grade.
| 週次 | 主題 |
|---|---|
| 第 1 週 | exterior measure, Lebesque measure |
| 第 2 週 | measureable function |
| 第 3 週 | Lebesque integral |
| 第 4 週 | Fubini's theorem |
| 第 5 週 | differentiation of the integral |
| 第 6 週 | good kernel and approximation to the identity |
| 第 7 週 | diffentiability of functions |
| 第 8 週 | diffentiability of functions rectifiable curves and the isoperimetric inequality |
| 第 9 週 | Hilbert space |
| 第 10 週 | Fourier series and Fatou's theorem |
| 第 11 週 | closed subspaces and orthogonal projections |
| 第 12 週 | linear transformations |
| 第 13 週 | compact operators |
| 第 14 週 | Fourier transform on L^2 |
| 第 15 週 | The Hardy space of the upper half plane |
Elias M. Stein & Rami Shakarchi, Real Analysis , Princeton University Press, 2005.
- 地點
- SA348
- 時間
- Thursday 16:00~17:00
- 聯絡方式
- Tel:56439