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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 |
106-2 |
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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 |
MATH2214 |
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課程識別碼 |
201 49660 |
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班次 |
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學分 |
5.0 |
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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 |
新數101新數101 |
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備註 |
限本系所學生(含輔系、雙修生)
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1062mathana |
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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 |
40% |
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3. |
homework, quizzes and (oral) performance in recitation |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/27, 3/1 |
~ Theorem 7.16: Uniform convergence and continuity and integration /sequences and series of functions. |
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第2週 |
3/6, 3/8 |
Theorem 8.1, 8.2, and 7.18 (Uniform convergence and differentiation/sequences and series of functions) |
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第3週 |
3/13, 3/15 |
Equicontinuous families of functions and the Stone-Weierstrass theorem (Sequences and series of functions) 第7章結束 |
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第4週 |
3/20, 3/22 |
Power series (Section 1 of Chapter 8), a Tauberian theorem, Raabe's test, and some basics of linear transformations (Chapter 9: Functions of several variables) |
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第5週 |
3/27, 3/29 |
~ Theorem 9.17 (differentiation and partial derivatives) |
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第6週 |
4/3, 4/5 |
No class (春假) |
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第7週 |
4/10, 4/12 |
Quiz 1 on 4/10. Inverse function theorem (Functions of several variables) |
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第8週 |
4/17, 4/19 |
Implicit function theorem and differentiation of integrals (Chpt. 9 Functions of several variables 授畢) |
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第9週 |
4/24, 4/26 |
The method of Lagrange's multipliers (不列入期中考範圍) |
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第10週 |
5/1, 5/3 |
1. Midterm on chapter 7, 8.1, and chapter 9 on 5/1, 2018 (Tuesday)
2. ⾃主學習週 No class on 5/3, 2018 |
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第11週 |
5/8, 5/10 |
Necessary and sufficient conditions for the existence of integral (Multiple Riemann integrals) |
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第12週 |
5/15, 5/17 |
Fubini's theorem (Multiple Riemann integrals) |
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第13週 |
5/22, 5/24 |
Change of variables (Multiple Riemann integrals) |
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第14週 |
5/29, 5/31 |
Gamma and Beta functions |
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第15週 |
6/5, 6/7 |
Fourier series I: L_2 theory |
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第16週 |
6/12, 6/14 |
Fourier series II: various convergence theorems (請以最新逐週公布的『課程大綱』為準。本週與以下之內容為系統複製105下之進度，供同學了解課程進行之快慢。爾後隨著課程進行將會逐週進行更新。） |
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第17週 |
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Fourier series, quiz on 6/18 and final on 6/23 9:10 - 12:10 |
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