必修課程介紹

• 預備知識：微積分、基礎數學、高等微積分
• 適合年級： 三年級
• 課程簡介：

複變函數論是一個重要的領域，在物理、數論、組合等...都有許多應用。複變函數論主要是學習解析方程，而在大學的學習範圍主要為其基礎的領域，包含解析方程、線積分、奇異值、殘值定理、保角映射、 解析延拓等...。

• 課程大綱：

1. Definition of Complex Numbers.
   
2. Topology of the Complex Plane.
   
3. Power Series.
   
4. Analytic Functions and Cauchy-Riemann Equations.
   
5. Line Integrals.
   
6. Closed Curve Theorem for Entire Functions.
   
7. Properties of Entire Functions.
   
8. Properties of Analytic Functions
   
9. Cauchy’s Theorem
   
10. Isolated Singularities.
    
11. Laurent Series.
    
12. The Residue Theorem.
    
13. Introduction into Conformal Mappings.
    
14. Riemann Mapping Theorem.
    
15. Analytic Continuation.

• 參考書目：

1. J. Bak and D. J. Newman (1999). Complex Analysis, Springer, corr. 2nd printing edition.
   
2. H. A. Priestley (2003). Introduction to Complex Analysis, OUP Oxford 2nd edition.