課程資訊
課程名稱
實分析二
Real Analysis (Ⅱ) 
開課學期
109-2 
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
選修 
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304天數304 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1092MATH7202_ 
課程簡介影片
 
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課程概述

Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. The first semester of this course will cover the following topics : set theory, functions of bounded variation, Riemann-Stieltjes integrals, Lebesgue measure theory, measurable functions, Lebesgue integration theory, differentiation theory and their applications. The topics in the second semester include function spaces with focus on the classical Lp spaces, convolution operators, abstract measures and some basic materials of Harmonic analysis such as Fourier series and fractional integrals as well as Poincare-Sobolev estimates. 

課程目標
This course aims to introduce basic theory and techniques of modern analysis.
Our goal in the second semester is to go through in details the text book from chapter 9 to chapter 15. 
課程要求
Real Analysis I 
預期每週課後學習時數
 
Office Hours
 
參考書目
1: Elias M. Stein and Rami Shakarchi, Real Analysis
2: G. Folland, Real Analysis: modern techniques and their applications
3: too many 
指定閱讀
Richard Wheeden and Antoni Zygmund, Measure and Integral: An Introduction to Real Analysis  
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Midterm exam 
30% 
 
2. 
Final exam 
30% 
 
3. 
Homework 
40% 
 
 
課程進度
週次
日期
單元主題