實變函數論(二)

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, general mathematical maturity

Wheeden, Richard L and Zygmund, Antoni , Measure and integral : an introduction to real analysis , M. Dekker, c1977.

(1) Class attendance: 1/5 of the final grade, (2) Assigned homework problems: 4/5 of the final grade,

• 1. Hilbert space 2.Abstract measure and integration theory 3. Ergodic theory 4. Hausdorff Measure 5. Fractals 6. L^p space

Elias M. Stein & Rami Shakarchi, Real Analysis , Princeton University Press, 2005.

地點

SA339

時間

Thursday 16:00~17:00

聯絡方式

Tel:56439