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課程名稱 |
分析導論二
Introduction to Mathematical Analysis(Ⅱ) |
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開課學期 |
103-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
張志中 |
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課號 |
MATH2210 |
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課程識別碼 |
201 49520 |
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班次 |
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學分 |
4 |
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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 |
星期二2,3,4(9:10~12:10)星期四3,4(10:20~12:10) |
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上課地點 |
天數102天數102 |
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備註 |
總人數上限：70人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1032mathana |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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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 |
sequences and series of functions, multivariable differential calculus, inverse and implicit function theorems, multiple Riemann integrals, and Lebesgue theory of measure and integration. |
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課程目標 |
While providing students with fundamental concepts of mathematical analysis, this course aims to cultivate the ability of dealing with abstract notions and rigorous proofs. Students are expected to work out solutions/proofs of exercises/homework, and to present their findings with precision and clarity in recitation in order to both improve communication skills, and fortify the understanding of the material. This course is considered relatively advanced, and a higher degree of commitment is recommended.
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課程要求 |
mathematical analysis I |
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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 |
Textbook. W. Rudin: Principles of mathematical analysis, 3rd edition, McGraw-Hill, 1976. |
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參考書目 |
1. T. M. Apostol: Mathematical analysis.
2. Marian Muresan: A concrete approach to classical analysis. CMS books in
mathematics. Springer 2009. |
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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. |
Midterm |
30% |
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2. |
Final |
30% |
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3. |
homework, quizzes and (oral) performance in recitation |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/24,2/26 |
~ Theorem 7.11: Uniform convergence and continuity/sequences and series of functions |
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第2週 |
3/03,3/05 |
Uniform convergence and integration and differentiation/sequences and series of functions |
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第3週 |
3/10,3/12 |
Sequences and series of functions |
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第4週 |
3/17,3/19 |
Sequences and series of functions |
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第5週 |
3/24,3/26 |
Linear transformations (Functions of several variables) |
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第6週 |
3/31,4/02 |
Functions of several variables |
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第7週 |
4/07,4/09 |
Inverse function theorem (Functions of several variables) |
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第8週 |
4/14,4/16 |
Implicit function theorem (Functions of several variables) |
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第9週 |
4/21,4/23 |
Review and quiz 2 |
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第10週 |
4/28,4/30 |
Midterm |
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第11週 |
5/05,5/07 |
No class (自主學習) |
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第12週 |
5/12,5/14 |
Existence of integral (Multiple Riemann integrals) |
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第13週 |
5/19,5/21 |
Fubini's theorem (Multiple Riemann integrals) |
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第14週 |
5/26,5/28 |
Change of variables (Multiple Riemann integrals) |
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第15週 |
6/02,6/04 |
Fourier series, term essay due |
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第16週 |
6/09,6/11 |
Fourier series |
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第17週 |
6/16,6/18 |
Fourier series, quiz on 6/18 and final on 6/23 9:10 - 12:10 |
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