Simple Complex Analysis

Author: Gong Sheng
Publisher:
Publish Date: 1999-11-01
Features: This book systematically presents the fundamental theories and methods of complex function theory. The book is divided into six chapters, covering topics such as calculus, the Cauchy integral theorem and Cauchy integral formula, Weierstrass series theory, the Riemann mapping theorem, differential geometry and the Picard theorem, and an introduction to functions of several complex variables. Each chapter is accompanied by a selection of exercises for readers. The book attempts to address the content of complex function theory from the perspective and methods of modern mathematics. For example: using preliminary knowledge of differential geometry to provide concise proofs of the Picard theorems; emphasizing the concept of transformation groups and utilizing the holomorphic automorphism group on simple regions to prove the Poincaré theorem; and offering a concise introduction to functions of several complex variables. The book is concise, accessible, rigorous in logic, and focuses on the connection between complex analysis content and modern mathematics, presenting traditional content in a new light. Since its publication in May 1996, the book has been widely welcomed by teachers and students due to its novel content, concise presentation, and ease of understanding. For this reprint, the author, based on the book's use as a textbook in several universities such as USTC and Tsinghua University, as well as his own teaching experience and insights, provides a profound elaboration on the writing intent and mathematical unity in the "Preface to the Reprint." Minor revisions have been made to the book's content, additional exercises have been added at the end of each chapter, and printing errors have been corrected to better serve teaching purposes. This book can serve as a textbook for undergraduate students in mathematics and applied mathematics departments, as well as a reference book for graduate students, teachers, and professionals in related fields. It is also suitable for researchers in complex analysis, real analysis, and related fields.