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課程名稱 |
實分析二
Real Analysis (Ⅱ) |
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開課學期 |
106-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
沈俊嚴 |
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課號 |
MATH7202 |
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課程識別碼 |
221 U2880 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期一1,2(8:10~10:00)星期三3,4(10:20~12:10) |
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上課地點 |
天數305天數305 |
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備註 |
研究所基礎課。
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1062MATH7202_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
The topics that we will cover in the second semester include:
(1) Function spaces with focus on the classical Lp spaces, some basic Fourier series and its connections to L^2 space.
(2) Convolution operators that allow us to study the approximation of identity.
(3) Generalization of Lebesgue integral to abstract measures integrals as well as the Hausdorff measure.
(4) Some materials of Harmonic analysis such as the convergence and divergence of Fourier series.
(5) If time permits, we will also study fractional singular integrals and it applications to PDE. |
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課程目標 |
Course Goal：To have fundamental knowledge of real variables theory.
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課程要求 |
Advanced Calculus; Elementary linear algebra
Midterm Exam 30%, Final Exam 30% and Homework 40%. |
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預期每週課後學習時數 |
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Office Hours |
備註： Office hours: Mondays 10 am -11:30 am |
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指定閱讀 |
Textbook: Wheeden and Zygmund, Measure and Integral, an introduction to real analysis. |
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參考書目 |
Reference books: (1) G. Folland, Real Analysis; (2) E. Stein & R. Shakarchi, Real Analysis. |
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評量方式
(僅供參考) |
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