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課程名稱 |
應用分析
APPLIED ANALYSIS |
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開課學期 |
99-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳宜良 |
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課號 |
MATH5410 |
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課程識別碼 |
221 U5600 |
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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 |
星期二1,2(8:10~10:00)星期四1(8:10~9:00) |
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上課地點 |
新502新502 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/991appl_analysis |
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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 |
(SOME STUDENTS REQUEST TO CHANGE THE SCHEDULE FROM THURSDAY 4 to THURSDAY 1.
I HAVE DONE IT.)
This course is designed as a basic analysis course between Advanced Calculus and Real Analysis.
The main purpose is to provide students basic functional analysis
background for studying applied mathematics, including partial differential equations, image science, inverse problems and computational mathematics.
I will mainly follow the lecture note written by John Hunter and Bruno Nachtergaele on Applied Analysis. This book is designed for one-year lecture.
I will cover Chapters 5-9 and 13. I will assume students know the material of Chapters 1-4. Normally, it is taught in the Advanced Calculus (for example, Rudin's book). You should check whether you have the background of Chapters 1-4 below.
The table of contents of this textbook is the follows.
Chapter 1: Metric and Normed Spaces (1-34)
Chapter 2: Continuous Functions (35-60)
Chapter 3: The Contraction Mapping Theorem (61-79)
Chapter 4: Topological Spaces (81-89)
*Chapter 5: Banach Spaces (91-123)
*Chapter 6: Hilbert Spaces (125-147)
*Chapter 7: Fourier Series (149-186)
*Chapter 8: Bounded Linear Operators on a Hilbert Space (187-214)
*Chapter 9: The Spectrum of Bounded Linear Operators (215-243)
Chapter 10: Linear Differential Operators and Green's Functions (245-286)
Chapter 11: Distributions and the Fourier Transform (287-333)
Chapter 12: Measure Theory and Function Spaces (335-377)
*Chapter 13: Differential Calculus and Variational Methods (379-426)
References (427-429)
The e-book is available on the website. |
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課程目標 |
This course is designed as a basic analysis course between Advanced Calculus and Real Analysis.
Its main purpose is to provide students basic analysis
background for studying applied mathematics, including partial differential equations, image science, inverse problems and computational mathematics.
For instance, many problems in image reconstruction and inverse problems need basic tool of functional analysis.
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課程要求 |
Linear Algebra, Advanced Calculus, Introduction to ordinary differential equations, Introduction to partial differential equations |
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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 |
John Hunter and Bruno Nachtergaele's e-book on Applied Analysis.
It is available by googling ``Pdf files of Applied Analysis.'' |
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參考書目 |
Frank Naterer and Frank Wubbeling, Mathematical Methods in Image Reconstruction, SIAM |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/14,9/16 |
Chapter 1: Metric and Normed Spaces (1-34) |
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第2週 |
9/21,9/23 |
Chapter 2: Continuous Functions
Chapter 3: Contraction Mapping |
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第3週 |
9/28,9/30 |
Chapter3: Contraction Maps |
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第4週 |
10/05,10/07 |
Chapter 5: Banach Spaces |
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第5週 |
10/12,10/14 |
Chapter 5: Banach Spaces |
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第6週 |
10/19,10/21 |
Chapter 6: Hilbert Spaces |
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第7週 |
10/26,10/28 |
Chapter 7: Fourier Series (149-186) |
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第8週 |
11/02,11/04 |
Chapter 7: Fourier Series (149-186) |
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第9週 |
11/09,11/11 |
Mid term exam,
No class on 11/11 |
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第10週 |
11/16,11/18 |
Chapter 8: Bounded Linear Operators on a Hilbert Space (187-214) |
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第11週 |
11/23,11/25 |
Chapter 8: Bounded Linear Operators on a Hilbert Space (187-214) |
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第12週 |
11/30,12/02 |
Chapter 9: The Spectrum of Bounded Linear Operators (215-243) |
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第13週 |
12/07,12/09 |
Chapter 9: The Spectrum of Bounded Linear Operators (215-243)
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第14週 |
12/14,12/16 |
No class on Dec. 14.
Chapter 13: Differential Calculus and Variational Methods (379-426) |
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第15週 |
12/21,12/23 |
Chapter 13: Differential Calculus and Variational Methods (379-426) |
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第16週 |
12/28,12/30 |
Chapter 13: Differential Calculus and Variational Methods (379-426) |
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第17週 |
1/04,1/06 |
Review and Final Exam |
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