實變函數論(一)

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

H. L. Royden, Real analysis , Collier-Macmillan Company, c1968.

(1) Class attendance: 1/10 of the final grade, (2) Assigned homework problems: 3/10 of the final grade, (3) Three midterm exams : 3/5 of the final grade.

• Preliminaries
• Preliminaries
• Functions of bounded variations
• Functions of bounded variations
• Lebesque and outer measure
• Lebesque and outer measure
• Lebesque and outer measure
• Lebesque measurable functions
• Lebesque measurable functions
• The Lebesque integral
• The Lebesque integral
• The Lebesque integral
• Repeated integral
• Repeated integral
• Differentiation
• Differentiation
• Differentiation
• Differentiation

Measure and integral: An introduction to real analysis Richard L Wheeden, Antoni Zygmund Taylor and Francis group, 1997.

地點

SA348

時間

Thursday 16:00~17:00

聯絡方式

Tel:56439