Complex Analysis
暫譯: 複變分析

1. 介紹
2. 解析函數及其性質
3. 奇異點、洛朗級數、留數
4. 保形映射、基本函數
5. 保形映射的基本原則、多邊形的變換

ANDREI BOURCHTEIN is Professor at the Institute of Physics and Mathematics, Federal University of Pelotas, Brazil. He received his Ph.D. in Mathematics and Physics from the Hydrometeorological Center of Russia. He began his academic and research career as an Associate Professor at Mathematics Institute, Far East State University, Russia, and a Research Scientist at the Hydrometeorological Institute, Russia. In 1995, he joined the Federal University of Pelotas, Brazil, as Associate Professor at the Institute of Physics and Mathematics before being promoted to Full Professor. An author of more than 100 refereed articles and 7 books, Prof. Bourchtein's research interests include real and complex analysis, numerical analysis, computational fluid dynamics and numerical weather prediction. During his research career, he was awarded a number of grants from Brazilian science foundations and scientific societies, including the International Mathematical Union (IMU) and the International Council for Industrial and Applied Mathematics (ICIAM).

LUDMILA BOURCHTEIN is Professor Emeritus and Senior Research Scientist at the Institute of Physics and Mathematics, Federal University of Pelotas, Brazil. She received her Ph.D. in Mathematics from Saint Petersburg State University, Russia. During the span of 34 years at the Mathematics Institute, Far East State University, Russia, she held different positions, from Assistant Professor, Associate Professor, to the rank of Full Professor. In the last 15 years, she served as Associate and Full Professor at the Institute of Physics and Mathematics, Federal University of Pelotas, where she was conferred with the title of Emeritus Professor in 2019. An author of more than 80 referred articles and 5 books, her research interests include real and complex analysis, conformal mappings and numerical analysis. During her research career, she was awarded a number of grants of Russian and Brazilian science foundations and scientific societies, including the International Mathematical Union (IMU) and the International Council for Industrial and Applied Mathematics (ICIAM).

安德烈·布爾赫廷（ANDREI BOURCHTEIN）是巴西佩洛塔斯聯邦大學物理與數學研究所的教授。他在俄羅斯水文氣象中心獲得數學與物理學的博士學位。他的學術與研究生涯始於俄羅斯遠東國立大學數學研究所的副教授及俄羅斯水文氣象研究所的研究科學家。1995年，他加入巴西佩洛塔斯聯邦大學，擔任物理與數學研究所的副教授，並於後來晉升為正教授。布爾赫廷教授是超過100篇經過審核的文章和7本書的作者，他的研究興趣包括實數與複數分析、數值分析、計算流體力學及數值天氣預報。在他的研究生涯中，他獲得了來自巴西科學基金會和科學社團的多項資助，包括國際數學聯盟（IMU）和國際工業與應用數學理事會（ICIAM）。

盧德米拉·布爾赫廷（LUDMILA BOURCHTEIN）是巴西佩洛塔斯聯邦大學物理與數學研究所的名譽教授及高級研究科學家。她在俄羅斯聖彼得堡國立大學獲得數學博士學位。在俄羅斯遠東國立大學數學研究所的34年中，她擔任過不同職位，從助理教授、副教授到正教授。在過去的15年中，她在巴西佩洛塔斯聯邦大學物理與數學研究所擔任副教授和正教授，並於2019年被授予名譽教授的稱號。她是超過80篇經過審核的文章和5本書的作者，她的研究興趣包括實數與複數分析、共形映射和數值分析。在她的研究生涯中，她獲得了來自俄羅斯和巴西科學基金會及科學社團的多項資助，包括國際數學聯盟（IMU）和國際工業與應用數學理事會（ICIAM）。