Holiday
GEN III綜三 201 M5M6R5R6
This course will cover the concept of holomorphic functions, Cauchy's integral formula. Maximum modulus principle for holomorphic functions shall be proved. Via calculus of residues, we show how to evaluate the line integral. Finally, we will discuss the conformal mapping and prove the fundamental Riemann mapping theorem.
Course keywords: 解析函數(holomorphic function), 柯西積分公式(Cauchy integral formula), 最大模數原理(maximum modulus principle), 調和函數(harmonic function), 保角映射(conformal mapping). 一、課程說明(Course Description) Basically we shall cover the following topics. (1)Cauchy-Riemann equation,Cauchy theorem for holomorphic functions, (2)Cauchy integral formula, (3)Maximum modulus principle, (4)Laurent series,meromorphic functions, (5)Calculus of residues, (6)Harmonic functions of two real variables, (7)Conformal mappings, Riemann mapping theorem, (8)Linear fractional transformation. 二、指定用書(Text Books) 程守慶:數學:我思故我在,華藝學術出版部,新北市,台灣,2022 三、參考書籍(References) 1. L. V. Ahlfors: Complex Analysis, . 2. E. M. Stein and R. Shakarchi: Complex Analysis, Princeton University Press. 3. R. E. Greene and S. G. Krantz: Function theory of one complex variable, John Wiley & Sons, INC. 4. W. Rudin: Real and Complex Analysis, McGraw-Hill Book Company. 5. R. P. Boas: Invitation to complex Analysis, McGraw-Hill, International Editions, 1992 四、教學方式(Teaching Method) Lecture and assignments. 五、教學進度(Syllabus) 六、成績考核(Evaluation) It will be announced in the first class. 七、可連結之網頁位址
MON | TUE | WED | THU | FRI | |
08:00108:50 | |||||
09:00209:50 | |||||
10:10311:00 | |||||
11:10412:00 | |||||
12:10n13:00 | |||||
13:20514:10 | |||||
14:20615:10 | |||||
15:30716:20 | |||||
16:30817:20 | |||||
17:30918:20 | |||||
18:30a19:20 | |||||
19:30b20:20 | |||||
20:30c21:20 |
Average Percentage 62.21
Std. Deviation 19.95
演習課時間為T19:00~21:00
數學系大學部3年級4年級優先,第3次選課起開放全校修習
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