課程大綱及進度表
開課系所
數學三開課學年
97開課學期
1課程名稱(中文)
複變數函數論課程名稱(英文)
COMPLEX ANALYSIS課程碼
C133800分班碼
先修科目或先備能力
CalculusAdvance Calculus
學分數
3開課教師
林君恆電話
65130Office Hours By Appointment
課程概述
Introductory course on complex variables.教學目標
This is an introduction class for complex analysis. Students will learn how to differentiate and integrate a function of complex variable and the corresponding analyticfunction theory for complex valued functions.
授課課程大綱明細
Review on complex numbersAnalytic functions
Cauchy-Riemann Equations
Harmonic functions
Exponential and Logarithmic functions. Branches and derivative of Log
Complex Integral
Cauchy-Goursat theorem, Cauchy integral formula, Maximum modulus principle
Series, Residues and Poles
Selected Topics (if time allows)
參考書目
Textbook: Complex Variables and Applications. Author:James Ward Brown, Ruel V.Churchill
Reference: Functions of one complex variable. Author: John B. Conway
Complex analysis. Author: Lars Ahlfors
課程要求
評量方式
Homework/Quiz 15%Midterm 35%
Final 50%