Brief Introduction to Complex Analysis

Author: Tan Xiaojiang
Publisher:
Publish Date: 2006-02-01
Features: This textbook is designed for the "Complex Analysis" course for mathematics majors in higher education institutions. Its prerequisite courses are Mathematical Analysis or Advanced Mathematics. The book is divided into eight chapters, covering topics such as: Complex Plane, Extended Complex Plane, Analytic Functions, Fractional Linear Transformations, Cauchy's Theorem, Cauchy's Formula, Power Series, Maximum Modulus Principle, Schwarz's Lemma, Laurent Series, Residues and Their Applications, Harmonic Functions, Analytic Continuation, and Riemann Existence Theorem, etc. In terms of content selection, the book emphasizes brevity and precision, highlighting the relationship between complex variables and real variables, as well as series and integral representations, to meet the needs of mathematics majors as much as possible and fully reflect the core content of complex analysis. In the treatment of content, it reflects the similarities and differences between real and complex analysis, focusing on rigorous proofs of theorems while considering the diverse backgrounds of readers learning advanced mathematics. The arrangement of content is gradual, progressive, and accessible, facilitating both teaching and self-study. The writing style is rigorous, concise, and clear. To broaden knowledge, the book also includes additional reading materials beyond the classroom. Additionally, each chapter is equipped with a sufficient number of exercises, and the answers or hints to some exercises are provided at the end of the book for reference. This book can serve as a textbook or teaching reference for undergraduate students in mathematics, physics, mechanics, and related disciplines. It can also be used as a reference for scientists and researchers engaged in mathematical or physical research.
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