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課程名稱 |
高等微積分二
Advanced Calculus (Ⅱ) |
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開課學期 |
100-2 |
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授課對象 |
數學系 |
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授課教師 |
陳金次 |
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課號 |
MATH2202 |
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課程識別碼 |
201 21320 |
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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 |
星期二3,4,@(10:20~)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 |
先修微積分。教學改善計畫課程有教學助理實施小班輔導。
總人數上限：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002AC2 |
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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 |
1.Real number system, Euclidean n-space
2.Point set topology: open and closed sets, boundary of a set, sequence and series
3.Compact and connected sets: Heine-Borel and Bolzano-Weierstrass theorems, path-connected and connected sets
4.Continuous mappings: boundedness of continuous functions on compact sets, intermediate-value theorem, uniform continuity
5.Differentiation: matrix representation, Taylor’s theorem, maxima and minima
6.Uniform convergence of sequence of functions: pointwise and uniform convergences, integration and differentiation of series, Arzela-Ascoli theorem, fixed point theorem, Stone-Weierstrass theorem, Dirichlet and Able test
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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 |
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 |
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參考書目 |
W. Rudin, Principle of Mathematical Analysis, 3rd edition.
T.M. Apostol, Mathematical Analysis, 2nd 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. |
第一次期中考 |
25% |
於第六周左右舉行 |
2. |
第二次期中考 |
25% |
於第十二周左右舉行 |
3. |
期末考 |
25% |
於期末考周舉行 |
4. |
平時成績 |
25% |
小考 |
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