Fall 2018 MATH 5200
Undergraduate Analysis 初等分析
Syllabus 課程大綱
宣導事項
- 9/12/2018: Welcome to the class!
教學進度
9/12/2018(星期三): Introduction/Motivation to Lebesgue Theory.
9/14/2018(星期五): General introduction to measure theory, existence of non-measurable set.
9/19/2018(星期三): Sigma algebras.
9/21/2018(星期五): Set functions and outer measures, basic properties.
9/26/2018(星期三): Basic Properties of outer measure.
9/28/2018(星期五): Construction of sigma algebra of measurable subsets.
10/3/2018(星期三): Borel sets, sets of measure 0.
10/5/2018(星期五): Measurable functions.
10/10/2018(星期三): 台灣國慶日放假。
10/12/2018(星期五): Approximations by simple functions, integrations, basic properties.
10/17/2018(星期三): Measure defined by integrals.
10/19/2018(星期五): Monotone convergence theorem.
10/24/2018(星期三): Fatou's lemma, dominated convergence theorem.
10/26/2018(星期五): Comparisons with Riemann integrals.
10/31/2018(星期三): Introduction to L^p spaces.
11/2/2018(星期五): Completeness of L^p spaces.
11/7/2018(星期三): Density of step functions in L^p.
11/9/2018(星期五): Midterm 1.
11/14/2018(星期三): Intdoduction to Hilbert spaces.
11/16/2018(星期五): Basic properties of Hilbert spaces.
11/21/2018(星期三): More properties of Hilbert spaces.
11/23/2018(星期五): Separability and orthonormality.
11/28/2018(星期三): Fourier series.
11/30/2018(星期五): Fourier series and convergences.
12/5/2018(星期三): Introduction to Fourier transforms.
12/7/2018(星期五): Convolutions.
12/12/2018(星期三): Fourier transforms and basic properties.
12/14/2018(星期五): Fourier transoforms for more general functions.
12/19/2018(星期三): Heat equation.
12/21/2018(星期五): Heat equation and Dirichlet problem.
12/26/2018(星期三): Signal analysis.
12/28/2018(星期五): Signal analysis and sampling theorem.
1/2/2019(星期三): Dispersion and Heisenberg's inequality.
1/4/2019(星期五): Quamtum mechanics and uncertainty principle.
作業
Homework 1 (截止日 9/28/2018 in Class):
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Solutions
Homework 2 (截止日 10/12/2018 in Class):
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Solutions
Homework 3 (截止日 11/9/2018 in Class):
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Solutions
Homework 4 (截止日 11/30/2018 in Class):
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Homework 5 (截止日 12/21/2018 in Class):
Folland Section 7.1: 2, 3, 4, 5, 8.
Folland Section 7.2: 2~7.
考試相關
講義