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課程名稱 |
複分析導論
Introduction to Complex Analysis |
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開課學期 |
104-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳金次 |
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課號 |
MATH5230 |
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課程識別碼 |
221 U6560 |
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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 |
必修 |
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上課時間 |
星期二6,7(13:20~15:10)星期四6,7(13:20~15:10) |
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上課地點 |
新302新302 |
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備註 |
複變函數論得用221 U6560複分析導論(4學分)替代。此課程研究生選修不算學分。
限學士班學生
總人數上限：75人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041MATH5230_cpxanls |
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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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課程概述 |
Complex function theory is a valuable tool used in many branches of pure, applied mathematics
and natural sciences, including geometry, number theory, partial di erential equations
and various topics in physics and engineering. A basic course shall enable students
to understand the concept of complex analyticity, to use residue calculus for evaluation of
integrals and to learn some additional topics (depending on available time) selected from
Riemann mapping theorem, special functions, prime number theorem, complex dynamical
systems, etc. |
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課程目標 |
Contents
Analytic functions of a complex variable and power series,
Cauchy's integral theorem,
maximum modulus principle and open mapping theorem,
singularities of analytic functions and Laurent series,
residue theorem and its applications: argument principle, Rouche's theorem and
the evaluation of integrals,
analytic continuation,
conformal mapping (on basic domains) and Schwarz lemma,
Weierstrass in nite products,
harmonic functions and the Dirichlet problem.
Selected topics: Riemann mapping theorem, Schwarz-Christo el integral, complex
dynamical systems, prime number theorem, elliptic functions, etc. |
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課程要求 |
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預期每週課後學習時數 |
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Office Hours |
另約時間 備註： 林耿弘助教 |
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指定閱讀 |
Joseph Bak • Donald J. Newman
Complex Analysis
(Third Edition) |
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參考書目 |
1. Stein, E.M., Shakarchi, R., \Complex analysis"
2. Lang, S., \Complex analysis", GTM 103
3. Ahlfors, L., \Complex analysis" |
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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. |
平時成績(小考) |
25% |
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2. |
期中考 |
35% |
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3. |
期末考 |
40% |
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