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課程名稱 |
複變函數論
Functions of a Complex Variable |
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開課學期 |
101-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
于 靖 |
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課號 |
MATH3201 |
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課程識別碼 |
201 31300 |
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班次 |
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學分 |
3 |
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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 |
星期二5,6(12:20~14:10)星期四5,6(12:20~14:10) |
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上課地點 |
新302新302 |
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備註 |
總人數上限：60人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1011complexanalysis |
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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 |
An introduction to the theory of analytic (holomorphic) functions of one complex variable. Studying domains (open connected subsets) in the (extended) complex plane, conformal transformations of planar domains. Line integrals as functions of arcs. Cauchy's theory. Calculus of Residues, Local properties of analytic functions. Power series. Harmonic Functions. Entire functions. Normal families of analytic functions. Euler's Gamma function. Riemann's zeta function. Elliptic functions, Picard's theorem, linear differential equations, Analytic continuations. |
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課程目標 |
Complex-valued functions on domains inside the complex plane. Basic general theory of these analytic functions. Line integrals as a tool. From the fundamental theorem of calculus to Cauchy's integral theorem. Power series as tool. Elementary functions. Special analytic functions and maps. Complex dynamical systems. Riemann's mapping theorem. |
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課程要求 |
Prerequisite : 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 |
L. V. Ahlfors, Complex Analysis, 3rd edition 1979, McGraw-Hill. |
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參考書目 |
I. Steward, Complex Analysis, 1983, Cambridge U. Press.
T. Needham, Visual Complex Analysis, 1997, Oxford U. Press. |
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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 1 |
30% |
200 min, written examination |
2. |
Mid-Term 2 |
30% |
200 min, written examination |
3. |
Final Exam |
40% |
200 min, written examination |
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