複變函數論
Complex Analysis
學期
111-2
學分
3
學分
當期課號
516709
永久課號
SCMA10021
開課單位
應用數學系
授課教師
千野由喜
校區
光復
類別
必修
上課時間表
| 節 | 週一 | 週四 |
|---|---|---|
2 09:00–09:50 | 複變函數論 SA320 | |
5 13:20–14:10 | 複變函數論 SA320 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
概述
We extend our knowledge of Analysis (Calculus) from the functions of real numbers to those of complex numbers. Mainly we will study Cauchy-Riemann equation, Cauchy's integral theorem, Cauchy's residue theorem.
先修科目
Calculus I & II
教學方式
TBA
評分方式
We will have Small Reports (70), Term-End Examination (30).
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Algebra of the complex plane |
| 第 2 週 | Topology of the complex plane: Limits for complex-valued functions |
| 第 3 週 | Topology of the complex plane: Continuity |
| 第 4 週 | Topology of the complex plane: Continuity and convergence for complex-valued functions |
| 第 5 週 | Power series |
| 第 6 週 | Differentiation in Complex Analysis: Cauchy-Riemann Equation |
| 第 7 週 | Elementary Functions |
| 第 8 週 | Integration in Complex Analysis |
| 第 9 週 | |
| 第 10 週 | Cauchy's Formula and Theorem |
| 第 11 週 | |
| 第 12 週 | Properties of analytic functions |
| 第 13 週 | Taylor Series and Analytic Continuation |
| 第 14 週 | Meromorphic Functions: Laurent Series |
| 第 15 週 | Residues |
| 第 16 週 | |
| 第 17 週 | |
| 第 18 週 |
教科書
This course is mainly constructed by the following book COMPLEX ANALYSIS (The Hitch hiker's Guide to the Plane) Second edition Ian Stewart and David Tall Cambridge University Press
Office Hours
- 地點
- TBA
- 時間
- TBA
- 聯絡方式
- Instructor (Yuki Chino): y.chino@math.nctu.edu.tw