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課程名稱 |
實分析二
Real Analysis (Ⅱ) |
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開課學期 |
101-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳俊全 |
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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 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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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102天數102 |
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備註 |
研究所基礎課。
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012RA |
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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 |
This course aims to present basic theory and techniques of modern analysis. |
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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 |
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課程要求 |
The prerequisites of this course are advanced calculus and real analysis I. |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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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.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
homework |
25% |
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2. |
midterm exam |
35% |
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3. |
final exam |
40% |
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