課程資訊
課程名稱
實分析二
REAL ANALYSIS (II) 
開課學期
96-2 
授課對象
理學院  數學系  
授課教師
李志豪 
課號
MATH7202 
課程識別碼
221 U2880 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期三5,6(12:20~14:10)星期五5,6(12:20~14:10) 
上課地點
新503新503 
備註
先修:高微及線代.研究所基礎課。
總人數上限:50人 
 
課程簡介影片
 
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課程概述

I. Contents:
In this course, we shall study theory of functions of real variables including Lebesgue measure and Lebesgue integral, differentiation and integration (Fubini’s Theorem, Radom-Nikodym Theorem,etc). We shall also study classical Banach spaces (L^p spaces and it dual spaces ), Hilbert spaces(spectral theorem of self-adjoint compact operators ,Riesz representation theorem, etc).
In the 2nd semester, we will review measure theory in and abstract measure theory. We plan to cover some elements of functional analysis, elements of Fourier analysis, Wavelets analysis, elements of distribution theory, Sobolev spaces, etc..
 

課程目標
To know the construction of measure and integration and the related application. 
課程要求
II. Course prerequisite:
Advanced Calculus, Linear Algebra
 
預期每週課後學習時數
 
Office Hours
 
參考書目
III. Reference material ( textbook(s) ):
H.L.Royden ,Real Analysis , (Third edition) , Prentice Hall, 1988.
R. Beals, Analysis-An Introduction, Cambbridge University Press, 2004.
R. L. Wheeden and A. Z. Zygmund, Measure and Integral, Marcel Dekker, INC
Gerald B. Folland, Real Analysis-Modern Techniques and their Applications, 2nd ed., John Willy & Sons, INC, 1999
 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework 
20% 
 
2. 
Midterm 
40% 
 
3. 
Final  
40% 
 
 
課程進度
週次
日期
單元主題