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課程名稱 |
分析導論一
Introduction to Mathematical Analysis(Ⅰ) |
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開課學期 |
103-1 |
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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 |
MATH2209 |
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課程識別碼 |
201 49510 |
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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202天數202 |
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備註 |
總人數上限：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031mathana |
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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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課程概述 |
Real number system, elementary point set topology of Euclidean and metric spaces, limit, continuity and derivatives of one variable functions, the Riemann-Stieltjes integral, infinite sequences and series of real numbers and functions, multivariable differential calculus, inverse and implicit function theorems, extreme value problems, and multiple Riemann integrals. |
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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 |
calculus |
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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 |
待補 |
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參考書目 |
Textbook. W. Rudin: Principles of mathematical analysis, 3rd edition,
McGraw-Hill, 1976.
Reference.
1. T. M. Apostol: Mathematical analysis.
2. Marian Muresan: A concrete approach to classical analysis. CMS books in
mathematics. Springer 2009 (find the e-book in NTU library) |
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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. |
期中考 |
30% |
暫定 |
2. |
期末考 |
30% |
暫定 |
3. |
作業、小考與演習課表現 |
40% |
暫定 |
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週次 |
日期 |
單元主題 |
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第1週 |
9/16,9/18 |
The real and complex number systems |
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第2週 |
9/23,9/25 |
Basic topology (cardinal number of real number system) |
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第3週 |
9/30,10/02 |
Basic topology (topological and metric spaces) |
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第4週 |
10/07,10/09 |
Basic topology (compactness, ...) |
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第5週 |
10/14,10/16 |
Perfect sets, connected sets. Chapter 3 Numerical sequences and series (convergent sequences in metric spaces, subsequences) |
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第6週 |
10/21,10/23 |
Numerical sequences and series. Quiz 1 (up to compact sets) Cauchy sequences, upper and lower limits, series (Cauchy condensation theorem) |
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第7週 |
10/28,10/30 |
Numerical sequences and series (Root and ratio tests, partial sum formula) |
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第8週 |
11/04,11/06 |
Numerical sequences and series (absolute convergence and rearrangement) |
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第9週 |
11/11,11/13 |
11/11 recitation, 11/13 Midterm |
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第10週 |
11/18,11/20 |
自主學習，停課一週 |
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第11週 |
11/25,11/27 |
Continuity |
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第12週 |
12/02,12/04 |
Continuity |
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第13週 |
12/09,12/11 |
Differential calculus |
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第14週 |
12/16,12/18 |
Differential calculus |
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第15週 |
12/23,12/25 |
The Riemann-Stieltjes integral |
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第16週 |
12/30,1/01 |
The Riemann-Stieltjes integral |
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第17週 |
1/06,1/08 |
The Riemann-Stieltjes integral. Recitation on 1/08 Thur. |
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