課程資訊
課程名稱
複變函數論
Functions of a Complex Variable 
開課學期
101-1 
授課對象
理學院  數學系  
授課教師
于靖 
課號
MATH3201 
課程識別碼
201 31300 
班次
 
學分
全/半年
半年 
必/選修
必修 
上課時間
星期二5,6(12:20~14:10)星期四5,6(12:20~14:10) 
上課地點
新302新302 
備註
總人數上限:60人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1011complexanalysis 
課程簡介影片
 
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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. 

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. 
課程要求
Prerequisite : Calculus. 
預期每週課後學習時數
 
Office Hours
 
參考書目
I. Steward, Complex Analysis, 1983, Cambridge U. Press.
T. Needham, Visual Complex Analysis, 1997, Oxford U. Press. 
指定閱讀
L. V. Ahlfors, Complex Analysis, 3rd edition 1979, McGraw-Hill. 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
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 
 
課程進度
週次
日期
單元主題