Complex Analysis (Paperback) (書況略舊,不介意在下單)

An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

這是一本針對具備高中程度複數知識的學生介紹複分析的書籍。它包含了十六個章節，前十一個章節針對大學高年級學生。後面的五個章節則是為了完整涵蓋通過複分析博士資格考試所需的背景知識。書中探討的主題包括茱莉亞集合和曼德博集合、狄利克雷級數和素數定理，以及黎曼曲面的均一化定理，並強調了球面、歐幾里得幾何和雙曲幾何三種幾何形式。全書的練習從簡單到具有挑戰性不等。本書是根據作者在多所大學（包括UCLA、布朗大學、布宜諾斯艾利斯的拉普拉塔大學和西班牙的瓦倫西亞自治大學）所進行的講座整理而成。