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課程名稱 |
分析導論一
Introduction to Mathematical Analysis(Ⅰ) |
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開課學期 |
107-1 |
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授課對象 |
社會科學院 經濟學系 |
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授課教師 |
陳俊全 |
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課號 |
ECON5129 |
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課程識別碼 |
323 U2030 |
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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 |
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備註 |
上課資訊依課號MATH2213訊息為主。限選修ECON課號，方可認定為經濟系選修課。
限學士班三年級以上 或 限碩士班以上
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1071ECON5129_MA_1 |
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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 |
Real number system, elementary point set topology of Euclidean and metric spaces, limit, compact and connected set, continuity, the Riemann-Stieltjes integral, infinite sequences and series of real numbers and functions, uniform convergence, multivariable differential calculus, inverse and implicit function theorems, extreme value problems, and multiple Riemann integrals and Fubini's Theorem. |
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課程目標 |
While providing students with fundamental concepts of mathematical analysis, this course aims to cultivate the ability to handle abstract notions and rigorous proofs.
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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 |
每週四 17:30~23:50
每週三 17:30~19:20
每週二 17:30~23:50
每週一 10:20~12:20 備註： 一:林自立(天數103) 二+四:王舜傑(天數455) 三:李雙言(天數103) |
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指定閱讀 |
待補 |
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參考書目 |
Textbook: Elementary Classical Analysis, 2nd Edition
by Jerrold E. Marsden and Michael J. Hoffman
Reference: Introduction to Analysis, 4th Edition
by William R. Wade
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/11,9/13 |
Introduction.
Logic, set and function.
The origin of numbers. |
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第2週 |
9/18,9/20 |
Natural numbers, integers and rational numbers.
Field axioms |
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第3週 |
9/25,9/27 |
Ordered fields.
Limits, Cauchy sequences and Completeness Axiom. |
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第4週 |
10/02,10/04 |
Construction of the real number system |
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第5週 |
10/09,10/11 |
Supremum, infimum
Properties equivalent to completeness axiom |
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第6週 |
10/16,10/18 |
Cantor's theory of infinity
Cardinality
Countable and uncountable |
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第7週 |
10/23,10/25 |
Shiroder-Bernstein's theorem
Fine properties of real numbers |
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第8週 |
10/30,11/01 |
cluster point, limsup, liminf
Vector space, norm, distance, inner product |
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第9週 |
11/06,11/08 |
Topology of the Euclidean space.
Open sets, interior points in a metric space. |
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第10週 |
11/13,11/15 |
midterm exam, school anniversary |
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第11週 |
11/20,11/22 |
sequence in a metric space, limit, cluster point |
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第12週 |
11/27,11/29 |
series in a metric space |
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第13週 |
12/04,12/06 |
sequentially compact: Heine-Borel Theorem |
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第14週 |
12/11,12/13 |
compact: open cover, totally bounded, Bolzano-Weierstrass Theorem |
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第15週 |
12/18,12/20 |
connected and path-connected sets, continuous mapping, operations on continuous mappings |
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第16週 |
12/25,12/27 |
images of compact and connected sets, maximum-minimum theorem, intermediate theorem |
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第17週 |
1/01,1/03 |
uniform continuity, Riemann integrable |
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