Fall 2017 MATH 2111
Advanced Calculus 1 高等微積分(一)
Syllabus 課程大綱
請踴躍填答教學評量
宣導事項
- 9/18/2017(星期一): Welcome to the class.
- 9/28/2017(星期四): HW2 非常態繳交時間,請特別注意
- 12/22/2017(星期五): 12/25/2017之演習課將挪用為12/20/2017老師缺席課堂之補課.
教學進度
9/18/2017(星期一): greeting and introduction to the course, natural and rational numbers.
9/20/2017(星期三): ordered fields, intuitive definition of R, some properties of R.
9/25/2017(星期一): real and complex numbers, more properties.
9/27/2017(星期三): countable sets.
10/2/2017(星期一): finish countable/uncountable sets, open/closed balls, open/closed sets.
10/4/2017(星期三): 中秋節放假.
10/9/2017(星期一): 台灣國慶日彈性放假.
10/11/2017(星期三): union/intersection of open/closed sets, interior.
10/16/2017(星期一): relative open subsets, introduction to compact sets.
10/18/2017(星期三): properties of compact sets.
10/23/2017(星期一): Heine-Borel Theorem.
10/25/2017(星期三): Perfect sets and Cantor set.
10/28/2017(星期一): Connected sets.
11/1/2017(星期三): Midterm exam 1.
11/6/2017(星期一): Topological spaces, sequences in metric spaces.
11/8/2017(星期三): Cauchy sequences, introduction to continuous functions.
11/13/2017(星期一): Continuity and topological properties.
11/15/2017(星期三): Uniform continuity, Cantor function.
11/20/2017(星期一): Introduction to sequences and series of functions.
11/22/2017(星期三): Uniform convergence, uniform convergence and continuity.
11/27/2017(星期一): Uniform convergence and interation/differentiation
11/29/2017(星期三): Theorem of Arzela-Ascoli.
12/4/2017(星期一): Speical Stone-Weierstrass Theorem.
12/6/2017(星期三): General Stone-Weierstrass Theorem.
12/11/2017(星期一): Complex Stone-Weierstrass Theorem.
12/13/2017(星期三): Midterm exam 2.
12/18/2017(星期一): Introduction to Power Series.
12/20/2017(星期三): 老師生病取消上課。
12/25/2017(星期一): Complex exponential and trigonometric functions.
12/27/2017(星期三): Fundamental Theorem of Algebra, brief motivation to Fourier analysis (heat equation).
1/1/2018(星期一): 元旦放假。
1/3/2018(星期三): Trigonometric series and Fourier series.
1/8/2018(星期一): Pointwise convergence of Fourier series.
1/10/2018(星期三): Parseval's Theorem, student presentation.
作業
若無另行宣布,第n組負責報告第n題。
Homework 0 (所有人皆須繳交,截止日9/20/2017):
Download here
Homework 1 (報告日9/25/2017演習課,截止日9/27/2017):
Download here. 報告截影. Solutions
Homework 2 (報告日10/11/2017 第3節(即第1節正課,截止日10/11/2017):
Download here. 報告截影. Solutions
Homework 3 (報告日10/16/2017, 截止日10/18/2017):
Download here. 部分報告截影. Solutions
Homework 4 (報告日10/23/2017, 截止日10/25/2017):
Download here. 報告截影. Solutions
Homework 5 (報告日10/30/2017, 截止日11/1/2017):
Download here. 部分報告截影. Solutions Part 1. Solutions Part 2
Homework 6 (報告日11/13/2017, 截止日11/15/2017):
Download here. 報告截影. Solutions Part 1. Solutions Part 2
Homework 7 (報告日11/20/2017, 截止日11/22/2017):
Download here. 報告截影. Solutions.
Homework 8 (報告日11/27/2017, 截止日11/29/2017):
Download here. 報告截影. Solutions.
Homework 9 (報告日12/4/2017, 截止日12/6/2017):
Download here. 報告截影. Solutions.
Homework 10 (報告日12/11/2017, 截止日12/13/2017):
Download here. 報告截影. Solution.
Homework 11 (截止日1/4/2018):
Download here.Solution.
Homework 12 (報告日1/8/2018, 截止日1/15/2018 本作業報告將指定講員,詳見分組資訊):
Download here.報告截影. Solutions for Non-Rudin Problems. Solutions for Rudin Problems.
分組資訊
本學期分組資訊
作業12指定講員
考試相關
講義
Sine as Infinite Produce (僅可在校園網路下載)