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課程名稱 |
實分析二
REAL ANALYSIS (II) |
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開課學期 |
96-2 |
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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 |
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503新503 |
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備註 |
先修:高等微積分及線性代數。研究所基礎課。
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 |
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..
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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 |
II. Course prerequisite：
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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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
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指定閱讀 |
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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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