課程大綱及進度表
開課系所
數學系開課學年
95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
C130900分班碼
先修科目或先備能力
微積分, 高等微積分學分數
3開課教師
劉瓊如電話
略Office Hours
略課程概述
Complex numbers, Analytic functions, Complex integration, Cauchy＇s theorem, Sequences and series of analyticfunctions, Residue theory, Conformal mapping
教學目標
讓大學生了解複數及複變函數的基本定理和 應用授課課程大綱明細
1. Complex numbers (i) The algebra and geometry of complex numbers (ii) Functions of a complex variable 2. Analytic functions (i) Continuity(ii) Complex derivatives (iii) The Cauchy-Riemann equations
3. Complex integration (i) Paths in the
complex plane (ii) Integrals along pathes
4. Cauchy＇s theorem (i) The local Cauchy theorem (ii) The global Cauchy theorems
5. Sequences and series of analytic functions (i) Sequences and series (ii) Sequences and series of analytic functions
6. Residue theory (i) Zeros of analytic functions (ii) the Residue theorem 7. Conformal mapping (i) conformal
mappings (ii) Mobius transformations (iii) Riemann＇s mapping theorem
參考書目
1. An introduction to complex function theory by Bruce P. Palka2. Fundamentals of Complex Analysis by E. B. Saff & A.D. Snider
3. Complex Analysis by J. Bak & D. J.
Newman
4. Functions of One Variable by J. B.
Conway
5. Function Theory of One Complex Variable by R. E. Greene & S. G. Krantz
