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課程名稱 |
泛函分析與逼近理論
Functional Analysis and Approximation Theory |
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開課學期 |
112-2 |
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授課對象 |
電機資訊學院 電信工程學研究所 |
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授課教師 |
戴邇立 |
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課號 |
CommE7006 |
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課程識別碼 |
942EM0330 |
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班次 |
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學分 |
3.0 |
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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 |
星期三6,7,8(13:20~16:20) |
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上課地點 |
博理212 |
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備註 |
本課程以英語授課。大學部學生欲修習請於加退選跟授課老師索取授權碼。
限碩士班以上
總人數上限：20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 |
This course provides graduate students with a panorama of functional analysis and approximation theory in multiple dimensions, adopting a systematic dual point of view (functions defined through a collection of measurements, weak formulations). The emphasis will be laid on the simplest, albeit modern mathematical concepts and mechanisms, with a view to avoid extraneous formalism and more abstract (e.g., topological) considerations.
This knowledge will be used to model engineering problems (e.g., data acquisition, sampling), to devise methods for solving exactly or approximately the inverse problems that are related (e.g., resulting from partial differential equations), and to analyze the error resulting from the approximations. |
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課程目標 |
Equip postgraduate students with advanced knowledge on functional analysis (in particular, on measure theory, integration and generalized functions), and on the approximation of functions using bases (in particular, polynomial, spline and wavelet approximations). At the end of this course, students are expected to be know how to deal with the measurements (generalized samples) of functions to construct accurate approximating functions. |
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課程要求 |
Grading: 5 Homeworks on
• Lebesgue integration (15%)
• Hilbertian Analysis (15%)
• Distribution Theory (15%)
• Calculus of Variations (15%)
• Approximation Theory (15%)
1 Matlab assignment on approximation theory and wavelets (20%)
Class participation (5%) |
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預期每週課前或/與課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
D.M.A. Bressoud, A radical approach to Lebesgue’s theory of integration, Cambridge University Press, (2008)
C.F. Gerald and P.O. Wheatley, Applied Numerical analysis, Addison-Wesley (1999)
Gel'fand, Izrail Moiseevich, et al. Generalized functions. Vol. 1. New York: Academic press, 1968.
D.C. Champeney, A handbook of Fourier theorems, Cambridge University Press (1987)
R. Dautray and J.L. Lions, Mathematical Analysis and Numerical Methods for Science and Technology: Functional and Variational Methods Springer (2000)
Mallat, Stéphane. A wavelet tour of signal processing. Access Online via Elsevier, 1999. |
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評量方式
(僅供參考) |
- 本校建議 A+ 比例上限為 20% ，非強制規定，授課教師可依課程要求調整，建議必修課程參考。
- 本校採用等第制評定成績，學生成績評量辦法中的百分制分數區間與單科成績對照表僅供參考，授課教師可依等第定義調整分數區間。詳見學習評量專區 (連結)。
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