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課程名稱 |
分析一
Analysis(Honor Program)(Ⅰ) |
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開課學期 |
106-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
林太家 |
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課號 |
MATH5232 |
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課程識別碼 |
221 U6540 |
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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 |
選修 |
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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101天數101 |
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備註 |
此課程研究生選修不算學分。
限學士班學生
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1061MATH5232_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
This is a course of mathematical analysis which provides solid training for mathematics majored students and students who are really interested in mathematical analysis. It provides the completely rigorous training in fundamental contents of mathematical analysis. Students are supposed to have the ability of writing rigorous mathematical arguments. |
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課程目標 |
A rigorous introduction to mathematical analysis. We will cover, in the first semester, most of the material in the textbook written by Marsden and Apostal, from the beginning topology of finite dimensional spaces, multivariable differential calculus, toward Fourier analysis. |
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課程要求 |
1. 需要預習且要經常上台報告
3. 部分內容可能以閱讀, 分組討論的形式進行.
4. 準時參加所有考試(共四次).
5. 熟悉數理邏輯，有自學的能力，能掌握一般數學定理的嚴格證明。
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
Marsden: Elementary Classical Analysis
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參考書目 |
Apostal: Mathematical Analysis
Stein & Shakarchi: I Fourier Analysis: An Introduction
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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. |
Test 1 |
10% |
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2. |
Test 2 (Midterm) |
20% |
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3. |
Test 3 |
20% |
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4. |
Final |
40% |
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5. |
Presentation |
10% |
Students will be assigned to study the proof of theorems by themselves. They will take turns presenting what they learn. |
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週次 |
日期 |
單元主題 |
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第2週 |
9/19,9/21 |
Chapter2, 3 |
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第3週 |
9/26,9/28 |
Chapter 3, 4 |
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第4週 |
10/03,10/05 |
Chapter 5 |
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第5週 |
10/10,10/12 |
10/12 習題課 |
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第6週 |
10/17,10/19 |
10/17 Test1, 10/19 Chapter 5 |
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第7週 |
10/24,10/26 |
10/24 Chapter 5; 10/26 Chapter 6 |
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第8週 |
10/31,11/02 |
10/31 Chapter 6; 11/02 Differentiation on function spaces |
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第9週 |
11/07,11/09 |
11/07 Bounded Variation; 11/09 習題課 |
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第10週 |
11/14,11/16 |
11/14 Test2; 11/16 自主學習 |
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第11週 |
11/21,11/23 |
Inverse Function Theory |
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第12週 |
11/28,11/30 |
11/28 Implicit Function Theory and its applications; 11/30 Integration and measure |
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第13週 |
12/05,12/07 |
12/05 measurable sets; 12/07 Lebesgue's Criterion, Fubini Theorem |
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第14週 |
12/12,12/14 |
12/12 習題課; 12/14 Test3 |
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第15週 |
12/19,12/21 |
12/19, 21 Change of Variable, Lebesgue Integral |
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第16週 |
12/26,12/28 |
12/26,28 Convergence in L^1 space |
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第17週 |
1/02,1/04 |
1/04 習題課 |
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第18週 |
1/09, 1/11 |
1/09 Final Exam |
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