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課程名稱 |
實分析二
Real Analysis (Ⅱ) |
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開課學期 |
102-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
劉豐哲 |
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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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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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課程概述 |
To prepare the students for their future studies in modern analysis and probability. |
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課程目標 |
A brief review of what covered in Real Analysis I, especially differentiation of functions of a real variable, functions of bounded variation and absolutely continuous functions, will be made first. Product measures, change of variables formula for integrals in Euclidean space, polar coordinates with application to potential integrals, basic principles of linear analysis and Hilbert space constitute the first part of the course content. The second part includes further study of L^p spaces, Fourier integral and Sobolev spaces with application to regularity of weak solutions of partial differential equations, and elements of probability theory. |
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課程要求 |
Advanced Calculus; Elementary linear algebra. |
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預期每週課後學習時數 |
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Office Hours |
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參考書目 |
1) G. B. Folland, Real Analysis; 2) S. L. Royden, Real Analysis; 3) S. Saks, Theory of Integral; 4) E. M. Stein & R. Shakarchi, Real Analysis. |
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指定閱讀 |
待補 |
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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. |
Mid-term examination |
30% |
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2. |
Final examination |
30% |
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3. |
Homework |
20% |
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4. |
Quizzes |
20% |
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