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課程名稱 |
高等微積分一
ADVANCED CALCULUS (I) |
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開課學期 |
97-1 |
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授課對象 |
數學系 |
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授課教師 |
陳俊全 |
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課號 |
MATH2201 |
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課程識別碼 |
201 21310 |
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班次 |
01 |
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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 |
新204新204 |
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備註 |
先修微積分。教學改善計畫課程有教學助理實施小班輔導，時段：二4。
限學號單號
總人數上限：80人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/971adv_cal |
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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 |
1.Real number system 2.Point set topology
3.Sequence and series 4.Continuity
5.Differentiation 6.The Riemann-Stieltjes integral
7.Sequence of functions |
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課程目標 |
Advanced calculus is a critical course for students who are seriously interested in mathematics or students who need knowledge of more deep analysis to deal with problems in various fields. In this course we present a theoretical basis of analysis suitable for students who have completed a course in elementary calculus. In this semester, several fundamental topics such as real number system, topology of the Euclidean spaces and metric spaces, continuity, uniform convergence, and differentiation and integration of one variable functions will be covered. |
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課程要求 |
Course prerequisite：Calculus
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預期每週課後學習時數 |
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Office Hours |
每週四 12:10~12:50
每週二 12:10~12:50 |
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指定閱讀 |
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參考書目 |
Walter Rudin：Principles of Mathematical Analysis. Third edition |
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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. |
Mid term exam |
35% |
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2. |
Final exam |
40% |
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3. |
Homework |
25% |
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週次 |
日期 |
單元主題 |
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第05週 |
10/13-10/17 |
1. countable and uncountable
2. metric space |
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第06週 |
10/20-10/24 |
1. open and closed sets
2. compact sets |
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第07週 |
10/27-10/31 |
compact sets |
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第08週 |
11/03-11/07 |
compact sets II |
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第09週 |
11/10-11/14 |
connected sets |
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第10週 |
11/17-11/21 |
sequences |
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第12週 |
12/01-12/05 |
Series |
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第14週 |
12/15-12/19 |
Continuity |
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第16週 |
12/29-01/02 |
Differentiation |
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第17週 |
01/05-01/09 |
Riemann-Stieltjes Integral |