標題: 實變函數論（一）Real Analysis I 作者: 吳培元Open Education Office開放教育推動中心 公開日期: 2010 摘要: 課程首頁 本課程是由交通大學應用數學系提供。 This is the course 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 analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems.課程目標/概述 This is the course 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 analysis developed in the 20th century and after. We will treat real analysis mainly in the first semester and functional analysis in the second. Hopefully, we can lay down a solid foundation for further usage in some other theoretical or applied area. After taking the course, the students are expected to have the general idea on the modern ways to attack the analysis problems. 課程章節 章節 內容綱要 第一章 Measure theory Abstract measure theory Lebesgue measure 第二章 Integration Convergence theorems (Monotone Convergence theorem, Dominated Convergence theorem, Fatou lemma) Fubini theorem Tonelli theorem Lpspace Completeness Compactness 第三章 Metric spaces Arzela-Ascoli theorem 課程書目 A. Friedman, Foundations of modern analysis, Dover, New York, 1982. 評分標準 項目 百分比 平時成績 1/3 期中考 1/3 期末考 1/3授課對象：碩士班學生預備知識：Advanced calculus and general mathematical maturity. URI: http://ocw.nctu.edu.tw/course_detail.php?bgid=1&nid=188http://hdl.handle.net/11536/108280 Appears in Collections: Open Course Ware