複變函數論
Complex Analysis
| 節 | 週二 | 週五 |
|---|---|---|
2 09:00–09:50 | 複變函數論 SA223（光復） | |
5 13:20–14:10 | 複變函數論 SA223（光復） 2 節連堂 | |
6 14:20–15:10 |
* 根據陽明交大上課時間表所列
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(Advanced) Calculus Reference: Principles of Mathematical Analysis by Walter Rudin
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TA: 王士銘 Office hours: 星期一晚上六點至八點(SC207)
Homeworks 30% Quizzes 10% Midterm exam 30% Final exam 30%
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction 2/27 Peace Memorial Day (a bridge holiday) |
| 第 2 週 | Chapter 1 Preliminaries to Complex Analysis - The Complex Plane 3/6 2026 Meichu Games (the course is suspended once) |
| 第 3 週 | Chapter 1 Preliminaries to Complex Analysis - Differentiability and Holomorphic Functions - Integration along Curves |
| 第 4 週 | Chapter 1 Preliminaries to Complex Analysis - Integration along Curves Chapter 2 Cauchy's Theorem and Its Applications - The Cauchy Integral Theorem - Goursat's proof |
| 第 5 週 | Chapter 2 Cauchy's Theorem and Its Applications - Local Existence of Primitives and Cauchy's Theorem in a Disc - Cauch's Integral Formulas - Liouville's Theorem |
| 第 6 週 | Children's Day and Tomb Sweeping Day |
| 第 7 週 | Chapter 2 Cauchy's Theorem and Its Applications - Power Series Expansion - Principle of Analytic Continuation - Morera's Theorem - Schwarz Reflection Principle |
| 第 8 週 | Chapter 2 Cauchy's Theorem and Its Applications - Sequences of Holomorphic Functions - Runge's Approximation Theorem |
| 第 9 週 | Chapter 2 Cauchy's Theorem and Its Applications - Runge's Approximation Theorem: proof of pole-pushing lemma April 24 (Fri), Midterm Exam |
| 第 10 週 | Labor Day |
| 第 11 週 | Chapter 3 Meromorphic Functions and the Logarithm - Zeros and Poles - The Residue Formula |
| 第 12 週 | Chapter 3 Meromorphic Functions and the Logarithm - The Residue Formula: Evaluation of Improper Integrals - Removable Singularities |
| 第 13 週 | Chapter 3 Meromorphic Functions and the Logarithm - Essential Singularities - Meromorphic Functions - The Argument Principle |
| 第 14 週 | Chapter 3 Meromorphic Functions and the Logarithm - Rouche's theorem - Open mapping theorem - Maximum/Minimal modulus principle - Schwarz lemma - Automorphisms of the disc |
| 第 15 週 | Chapter 3 Meromorphic Functions and the Logarithm - The complex logarithm - Integration along a branch cut |
| 第 16 週 | Chapter 3 Meromorphic Functions and the Logarithm - Homotopies and simply connected domains June 12 (Fri), Final Exam |
Textbook: Complex Analysis by Elias M.Stein and Rami Shakarchi, Princeton University Press References: Complex Analysis, Third Edition by Joseph Bak, Donald J. Newman. Complex Analysis, Third Edition by Lars Ahlfors Complex Analysis, Second Edition by Ian Stewart and David Tall
- 地點
- SA238
- 時間
- 教師未提供此項資料
- 聯絡方式
- E-mail: sswangtw@nycu.edu.tw