課程資訊
 課程名稱 實分析一Real Analysis (Ⅰ) 開課學期 112-1 授課對象 理學院  應用數學科學研究所 授課教師 陳逸昆 課號 MATH7201 課程識別碼 221 U2870 班次 學分 3.0 全/半年 半年 必/選修 必修 上課時間 星期一3,4(10:20~12:10)星期三3,4(10:20~12:10) 上課地點 天數101天數101 備註 總人數上限：65人外系人數限制：20人 課程簡介影片 核心能力關聯 核心能力與課程規劃關聯圖 課程大綱 為確保您我的權利,請尊重智慧財產權及不得非法影印 課程概述 The first semester of this course will cover the following topics : 1. Measure Theory: outer measure, Caratheodory outer measures, n-dimensional Lebesgue measure 2. Integration Theory: measurable functions, Lebesgue integral, monotone convergence and Lebesgue dominated convergence theorem, Fubini’s theorem 3. Elements of Functional Analysis: Baire Category Theorem and its consequences, open mapping theorem and closed graph theorem, separation principles and Hahn-Banach theorem, Hilbert spaces The topics in the second semester will include: 4. Differentiation and Integration: Hardy-Littlewood maximal function, Lebesgue differentiation theorem, functions of bounded variation, absolutely continuous functions, differentiability of functions 5. L^p spaces 6. Abstract Measure and Signed Measures: absolute continuity, Radon-Nikodym Theorem 7. Convolution operators and Fourier Transform 課程目標 Course Goal：This course aims to introduce basic theory and techniques of modern analysis. 課程要求 Introduction to Mathematical Analysis I, II; Linear Algebra 預期每週課後學習時數 Office Hours 指定閱讀 參考書目 (1) Fon-Che Liu, Real Analysis, Oxford University Press (2) Elias M. Stein and Rami Shakarchi, Real Analysis 評量方式(僅供參考)
 課程進度
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