Complex Analysis Introduction

Author: Li Zhong
Publisher:
Publish Date: 2004-11-01
Features: Introduction to Complex Analysis This textbook is designed for senior undergraduate students and graduate students in mathematics programs at comprehensive universities and normal universities. Its purpose is to present some fundamental theories and recent important developments in modern complex analysis (excluding several complex variables). The book is divided into nine chapters, with main content including: normal families and the Riemann mapping theorem, classical geometric function theory, conformal modulus and extremal length, quasiconformal mappings, basic concepts of Riemann surfaces, the Riemann-Roch theorem and the monodromy theorem, and Teichmüller theory and moduli spaces. These topics have deep connections with many branches of modern core mathematics. Therefore, the book is not only intended for students majoring in complex analysis but also for students in related fields. The book is based on the author's lecture notes used for many years, with concise and accessible language, clear emphasis, and a focus on explaining the significance of important concepts and the essence of methods. Some proofs of theorems have their own distinct features. The book provides necessary introductions and reviews on the historical development of some important theories and their connections with other fields. This book can serve as a textbook for senior undergraduate and graduate students in complex analysis at universities and colleges, as well as a reference book for researchers in related fields.