課程名稱 |
實分析二 Real Analysis (Ⅱ) |
開課學期 |
101-2 |
授課對象 |
理學院 數學系 |
授課教師 |
陳俊全 |
課號 |
MATH7202 |
課程識別碼 |
221 U2880 |
班次 |
|
學分 |
3 |
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102天數102 |
備註 |
研究所基礎課。 總人數上限:60人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012RA |
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 |
This course aims to present basic theory and techniques of modern analysis. |
課程目標 |
In this semester, we will focus on the following topics:
1. Differentiation theorems for BV and absolutely continuous functions,
rectifiable curves and isoperimetric inequality
2. Hilbert space, Banach space, Hahn-Banach theorem, closed graph theorem
3. L^p spaces,
4. Abstract measure and integration theory
5*. Hausdorff measure and fractals
6*. Fourier series and Fourier transform |
課程要求 |
The prerequisites of this course are advanced calculus and real analysis I. |
預期每週課後學習時數 |
|
Office Hours |
|
指定閱讀 |
|
參考書目 |
[1]. Real Analysis, Elias M. Stein and Rami Shakarchi
[2]. Measure and Integral: An Introduction to Real Analysis, Richard Wheeden and Antoni Zygmund.
[3]. Analysis, Elliott H. Leib and Michael Loss.
[4]. Real and Complex Analysis, Walter Rudin.
|
評量方式 (僅供參考) |
No. |
項目 |
百分比 |
說明 |
1. |
homework |
25% |
|
2. |
midterm exam |
35% |
|
3. |
final exam |
40% |
|
|
|