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課程名稱 |
泛函分析
FUNCTIONAL ANALYSIS |
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開課學期 |
94-2 |
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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 |
MATH5216 |
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課程識別碼 |
221 U3900 |
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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 |
新數103 |
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備註 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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. Metric Spaces
1. Locally compact and compact Sets.
2. Baire Category
3. The Ascoli- Arzela’ theorem
Chapter 2. 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 3. Banach spaces
1. Normed vector spaces. Hahn-Banach theorem.
2. Uniform boundedness principle. Open mapping principle. Closed graph theorem. Closed operators.
3. Compact operators. Fredholm alternative theorem.
4. Spectral theorem for bounded linear operators.
Chapter 4. Frechet Space, Introduction to Theory of Distribution
Definitions and Examples, Operations on Distributions, Fourier Transform, Applications to Partial Differential Equations.
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課程目標 |
Course Goal：
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 |
Course prerequisite：
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. R.Courant & D. Hilbert, Methods of Mathematical Physics, Vol. I.
4. Douglas N. Arnold, Functional Analysis, http://www.math.psu.edu/dna/
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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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