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課程名稱 |
高等微積分優一
Honors Advanced Calculus (Ⅰ) |
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開課學期 |
102-1 |
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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 |
MATH2207 |
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課程識別碼 |
201 49470 |
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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 |
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 |
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。數學系微積分成積A或A+或微積分甲A+
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1021AdCsH1 |
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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 |
Advanced Calculus is generally regarded as the most basic and solid training for mathematics majored students. In contrast to Calculus, it provides the completely rigorous training in "writing proofs". Also instead of intuition, it is based on general topology and real number system to develop the mathematical analysis. It is the foundation to all analytic methods.
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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). |
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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. |
Test1 |
20% |
10/17 |
2. |
Test2 (Midterm) |
20% |
11/7 |
3. |
Test3 |
20% |
12/3 |
4. |
Test4 (Final) |
20% |
1/2 |
5. |
Presentation |
20% |
Students will be assigned to study the proof of theorems by themselves. They will take turns presenting what they learn in every Tuesday class. |
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週次 |
日期 |
單元主題 |
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第1週 |
9/10,9/12 |
Topology of R^n |
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第2週 |
9/17,9/19 |
9/17 presentation, 中秋假期
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第3週 |
9/24,9/26 |
compact and connected sets |
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第4週 |
10/01,10/03 |
operations on continuous mapping |
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第5週 |
10/08,10/10國慶曰 |
uniform continuity (chap 4) |
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第6週 |
10/15,10/17 |
Test 1(10/17), 習題課10/15 |
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第7週 |
10/22,10/24 |
uniform convergence and continuous function spaces |
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第8週 |
10/29,10/31 |
Arzela-Ascoli and Stone-Weierstrass Theorems (chap 5) |
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第9週 |
11/05,11/07 |
Midterm, 習題課 |
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第10週 |
11/12,11/14 |
Differentiable Mapping |
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第11週 |
11/19,11/21 |
Functions of Bounded Variation (Apostal, Chapter 6) |
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第12週 |
11/26,11/28 |
Implicit Function Theorem, 習題課11/28 |
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第13週 |
12/03,12/05 |
Integration, Test 3, 12/3 |
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第14週 |
12/10,12/12 |
Fubini Theorem |
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第15週 |
12/17,12/19 |
The Lebesgue Integral (Apostal, Chapter 10) |
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第16週 |
12/24,12/26 |
Fourier Series (Apostal, Chapter 11), 習題課12/26 |
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第17週 |
12/31,1/02 |
12/31 上課, Final(1/2) |
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