An introduction to complex analysis

Huaixin Cao, Jianhua Zhang, Zhengli Chen, Zhihua Guo

Parution le 26/12/2025

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Résumé

An Introduction to Complex Analysis is a textbook focusing on the fundamental theories and methods of complex analysis. Guided by the core logic of "from basic construction to in-depth application," it systematically presents the key concepts and structure of the discipline. The book helps readers shift their perspective from the real number field to the complex number field, master the essential ideas and tools for studying complex functions, and build a solid foundation for further study in advanced complex analysis and related interdisciplinary fields such as physics, engineering, and mathematical physics.Divided into seven chapters, the book features a clear and coherent content framework. It strikes a balance between theoretical rigor and practical learning: each key concept is introduced with precise definitions and intuitive explanations; important theorems are accompanied by detailed proofs; and targeted exercises at the end of each chapter help reinforce understanding.While maintaining academic depth, the text remains accessible to beginners by avoiding excessive technical complexity. This book is ideal as an introductory textbook for junior undergraduate students majoring in mathematics. It also serves as a valuable reference for students in physics, electronics, and engineering, as well as for researchers in related fields interested in the core theories and practical applications of complex analysis.