Complex Analysis (Upgrading to Bachelor's Degree)

Author: Yang Linsheng
Publisher:
Publish Date: 2002-09-01
Features: This book is divided into eight chapters, covering Complex Numbers, Complex Functions, Analytic Functions, Complex Integration, Series Expansion of Analytic Functions, Residues, Conformal Mapping, and Analytic Continuation. The first four chapters form Part I, focusing on the properties of analytic functions and complex integration. They are based on the Cauchy Integral Theorem and use complex integration as a tool to further study important properties such as the isolated nature of zeros of analytic functions and the Uniqueness Theorem. The second part is the series expansion of analytic functions, including Taylor expansion and Laurent expansion, which are used to study the properties of analytic functions in the neighborhood of isolated singularities and the distribution of function values. The third part covers residues and their applications. The fourth part is the geometric theory of analytic functions—conformal mapping. The fifth part is analytic continuation. The content of this book progresses from simple to complex, with a clear focus and detailed explanations, making it convenient for self-study. It is suitable as a textbook for secondary school teachers and students of mathematics at various types of higher education institutions for upgrading purposes, as well as for the Engineering Mathematics course on "Complex Analysis."