課程資訊
課程名稱
實分析二
Real Analysis (Ⅱ) 
開課學期
106-2 
授課對象
理學院  數學研究所  
授課教師
沈俊嚴 
課號
MATH7202 
課程識別碼
221 U2880 
班次
 
學分
3.0 
全/半年
半年 
必/選修
必修 
上課時間
星期一1,2(8:10~10:00)星期三3,4(10:20~12:10) 
上課地點
天數305天數305 
備註
研究所基礎課。
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1062MATH7202_ 
課程簡介影片
 
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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. 

課程目標
Course Goal:To have fundamental knowledge of real variables theory.
 
課程要求
Advanced Calculus; Elementary linear algebra

Midterm Exam 30%, Final Exam 30% and Homework 40%. 
預期每週課後學習時數
 
Office Hours
備註: Office hours: Mondays 10 am -11:30 am 
參考書目
Reference books: (1) G. Folland, Real Analysis; (2) E. Stein & R. Shakarchi, Real Analysis. 
指定閱讀
Textbook: Wheeden and Zygmund, Measure and Integral, an introduction to real analysis.  
評量方式
(僅供參考)
   
課程進度
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日期
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