Complex Analysis
Complex Analysis
复制标题
复杂分析
DOI：
10.1007/978-0-387-21607-2
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Gamelin
中科院分区：
文献类型：
--
作者：
T. Gamelin
这本书提供了一个介绍复杂的分析为学生与一些熟悉复数从高中。这本书由三部分组成。第一部分是复分析课程的基本核心内容。第二部分包括各种更专门的主题作为论点的原则，施瓦茨引理和双曲几何，泊松积分，和黎曼映射定理。第三部分包括一系列主题，旨在完成通过复杂分析博士资格考试所需的所有背景。选定的主题包括Julia集和Mandelbrot集，Dirichlet级数和素数定理，以及黎曼曲面的单值化定理。三个几何，球形，欧几里得，双曲，强调。练习的范围从非常简单到相当具有挑战性，在所有章节。这本书是根据作者多年来在几个地方的讲座，特别是佩鲁贾的大学间暑期学校（意大利），以及加州大学洛杉矶分校，布朗大学，瓦伦西亚（西班牙）和拉普拉塔（阿根廷）。作者是明尼苏达州人，本科在耶鲁大学，研究生在加州大学伯克利分校。在麻省理工学院和拉普拉塔国立大学（阿根廷）呆了一段时间后，他于1968年加入加州大学洛杉矶分校。作者发表了一些研究文章和几本书的功能分析和解析函数理论。他目前参与加州K-12教育领域。
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The book consists of three parts. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics selected include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, particularly the Interuniversity Summer School at Perugia (Italy), and also UCLA, Brown University, Valencia (Spain), and La Plata (Argentina). A native of Minnesota, the author did his undergraduate work at Yale University and his graduate work at UC Berkeley. After spending some time at MIT and at the Universidad Nacional de La Plata (Argentina), he joined the faculty at UCLA in 1968. The author has published a number of research articles and several books on functional analysis and analytic function theory. he is currently involved in the California K-12 education scene.