課程概述 本課程介紹泛函分析的基本要素。我們將著重 Sobolev 空間 及線性算子理論. 我們將討論 Hahn-Banach theorem, principle of uniform boundedness 及 open mapping theorem. 我們也將討論 Riesz theory 及Fredholm theory.
We study some basic elements of functional analysis including some operator theory. The main objects in this course are Sobolev spaces and linear operators. We will discuss the Hahn-Banach theorem, the principle of uniform boundedness and open mapping theorem. Also, Riesz theory and Fredholm theory will also be discussed.
教學目標 We expect to grab the basic idea and concept of Constructive mathematics in modern mathematical language, Function spaces, and operators. Then we learn various properties of them from different aspects.
授課課程大綱明細
Ch1: Banach Contraction Fixed Point Theorem
Ch2: Banach Spaces
Ch3: Hilbert Spaces
Ch4: Midterm exam.
Ch5: Hahn–Banach Theorem
Ch6: Principle of Uniform Boundedness
Ch7: Open Mapping Theorem
Ch8: Differential and Integral Calculus in Banach Spaces
Ch9: Spectral Theory with Applications
Ch10: Final Exam.
參考書目 Functional Analysis and Applications, Abul Hasan Siddiqi, 2019, 1, 978-981-10-3725-2, Springer
課程要求 Real Analysis and Partial Differential Equations
評量方式 Homework: 40%
Final: 60%
學習規範 Course Policy
請遵守智慧財產權觀念不得不法影印
Please follow the Intellectual Property instruction and No illegal copy
1. 作業不能遲交。
2. 缺考需要醫師證明、或家長證明、或學校公假單。
3, 考試違規，報請學校處理。
課程網址 http://www.math.ncku.edu.tw/~fang
- 教師(teacher): 方永富