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課程名稱 |
實分析一
REAL ANALYSIS (I) |
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開課學期 |
96-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
李志豪 |
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課號 |
MATH7201 |
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課程識別碼 |
221 U2870 |
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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 |
星期三5,6(12:20~14:10)星期五5,6(12:20~14:10) |
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上課地點 |
新403新403 |
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備註 |
先修高微,線代
總人數上限：50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 |
In this course, we shall study theory of functions of real variables including Lebesgue measure and Lebesgue integral, differentiation and integration (Fibini’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 plan to cover some elements of functional analysis, elements of Fourier analysis, Wavelets analysis, elements of distribution theory,etc.
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課程目標 |
To know the construction of measure and integration and the related application.
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課程要求 |
建議先修
Advanced Calculus, 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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指定閱讀 |
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參考書目 |
Gerald B. Folland, Real Analysis-Modern Techniques and their Applications, 2nd ed., John Willy & Sons, INC, 1999
H.L.Royden ,Real Analysis , (Third edition) , Prentice Hall, 1988.
R. Beals, Analysis-An Introduction, Cambbridge University Press, 2004.
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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 |
20% |
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2. |
Midterm |
40% |
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3. |
Final |
40% |
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