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課程名稱 |
應用分析
Applied Analysis |
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開課學期 |
102-1 |
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授課對象 |
理學院 應用數學科學研究所 |
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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 |
必修 |
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上課時間 |
星期五2,3,4(9:10~12:10) |
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上課地點 |
天數304 |
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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/1021AppliedAnalysis |
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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 |
This one-semester course is designed as a basic analysis course after Advanced Calculus. It can be taken parallel to or prior to real analysis. The main purpose is to provide students (majored in applied mathematics, physics, engineering) basic background on functional analysis for studying applied mathematics, including partial differential equations, image science, inverse problems, numerical PDEs and computational mathematics.
I will mainly follow my own lecture note supplemented by the lecture note on Applied Analysis written by John Hunter and Bruno Nachtergaele. There is a digital version of the lecture notes.
The main applications includes the spectral theory of Sturm-Liouville systems, Some local existence theory by contraction mapping, direct method for calculus of variations.
THe contents include
• Chapter 1: Motivation: Problems from Calculus of Variations
• Chapter 2: Metric spaces, Banach Spaces, Hilbert Spaces
• Chapter 3: The Contraction Mapping Theorem with Applications
• Chapter 4: Approximation in Hilbert spaces, Fourier Series
• Chapter 5: Bounded Linear Operators on a Hilbert Space and Spectral Theory
• Chapter 6: Basic Calculus of Variations. |
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課程目標 |
• Students should understand the basic functional analysis with applications
• For each analytic technique taught in the class, students should find the simplest example and
understand it deeply.
• Students should be able to explain the esential idea with examples. |
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課程要求 |
Linear Algebra
Advanced Calculus
Ordinary Differential Equations |
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預期每週課後學習時數 |
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Office Hours |
備註： Friday 2:00-3:00 |
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指定閱讀 |
1. My own lecture note
2. John Hunter and Bruno Nachtergaele, Applied Analysis |
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參考書目 |
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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 |
40% |
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2. |
midterm |
30% |
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3. |
final |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
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Chapter 1: Motivation: Problems from Calculus of Variations |
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第2週 |
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Chapter 1: Motivation: Problems from Calculus of Variations |
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第3週 |
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Chapter 2: Metric spaces, Banach Spaces, Hilbert Spaces |
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第4週 |
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Chapter 2: Metric spaces, Banach Spaces, Hilbert Spaces |
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第5週 |
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Chapter 3: The Contraction Mapping Theorem with Applications |
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第6週 |
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Chapter 3: The Contraction Mapping Theorem with Applications |
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第7週 |
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Chapter 4: Approximation in Hilbert spaces, Fourier Series |
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第8週 |
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Chapter 4: Approximation in Hilbert spaces, Fourier Series |
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第9週 |
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Mid term exam,
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第10週 |
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Chapter 4: Approximation in Hilbert spaces, Fourier Series |
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第11週 |
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Chapter 5: Bounded Linear Operators on a Hilbert Space and Spectral Theory |
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第12週 |
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Chapter 5: Bounded Linear Operators on a Hilbert Space and Spectral Theory |
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第13週 |
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Chapter 5: Bounded Linear Operators on a Hilbert Space and Spectral Theory |
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第14週 |
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Chapter 5: Bounded Linear Operators on a Hilbert Space and Spectral Theory |
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第15週 |
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Chapter 6: Basic Calculus of Variations. |
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第16週 |
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Chapter 6: Basic Calculus of Variations. |
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第17週 |
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Review and Final Exam |
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