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課程名稱 |
泛函分析二
FUNCTIONAL ANALYSIS (II) |
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開課學期 |
97-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
李志豪 |
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課號 |
MATH7206 |
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課程識別碼 |
221 U0120 |
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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 |
星期五6,7,8(13:20~16:20) |
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上課地點 |
新405 |
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備註 |
先備知識：線代、高微。
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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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 |
Chapter 1. Review of some basic theorems in Metric Spaces and Banach spaces already covered in the 1st semester.
Chapter 2. Review some basic theorems in Hilbert Spaces
1. Orthogonal projections. Orthonormal basis. Bessel inequality. Fourier expansion.
2. Riesz representation theorem.
3. Spectral theory for positive operators and Sturm-Liouville problem.
4. Spectral theory for compact self-adjoint operators and integral equations of Fredholm type.
5. Spectral theory for self-adjoint operators.
Chapter 4. Frechet Space, Introduction to Theory of Distribution---
Definitions and Examples, Operations on Distributions
Chapter 4 : Fourier Analysis
Fourier Transform, Fourier Series, Sobolev Spaces, Applications to Partial Differential Equations.
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課程目標 |
1.Learning some basic abstract spaces：Metric Spaces, Hilbert Spaces, Banach Spaces, Frechet Spaces, etc.
2. Knowing some example, e.g. L Space, Sobolev Space, Schwartz Space, etc.
3. Knowing the theory and examples of the transformation of the Spaces as above.
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課程要求 |
預備知識為「高等微積分」、「線性代數」，最好曾修過「實變函數論」或相當課程。 |
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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. H. L. Royden, Real Analysis (3rd ed.)
2. Peter Lax, Functional Analysis, 2002 Wiley-Interscience.
3. Fon-Che Liu:實分析課程講義
http://www.math.sinica.edu.tw/www/file_upload/maliufc/maliufc-c.htm
4. Douglas N. Arnold, Functional Analysis, http://www.math.psu.edu/dna/
4. H. Dym;H. P. McKean, Fourier series and integrals, Academic Press,1972
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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. |
習題 |
20% |
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2. |
期中考 |
40% |
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3. |
期末考 |
40% |
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