Complex Analysis and Dynamics in One Variable with Applications 2024th Edition

“Throughout the book, historical remarks are included to situate results and concepts, and many topics are motivated by their role in other areas of mathematics or in applications. The style is formal but pedagogical, with proofs presented in full detail and terminology carefully defined. … It can serve as the main text for a one- or two-semester course, or as a reference for advanced undergraduates, graduate students, and researchers interested in the analytic and geometric foundations of complex dynamics.” (Tao Chen, Mathematical Reviews, April, 2026)

This textbook has been designed to support the initial study of Complex Analysis, progressing to Complex Dynamics. It focuses on the fundamental aspects of one-variable complex functions, covering the geometric theory and dynamics of iterations of rational mappings. Following the standard material, the book delves into an extensive range of advanced topics, encompassing the requirements for a one-year graduate-level course or a preliminary exam.

In this work, the reader will discover three distinctive characteristics: it simplifies and unifies ideas and concepts that might appear disparate or complicated in real analysis; it contributes to the development of other areas in mathematics; and it showcases relevance for applications in Science and Engineering, with many exercises. Historical notes throughout the text help to contextualize the theory.

With its flexible structure, this textbook provides a solid foundation for a first course in Complex Analysis and for a second more advanced course, establishing a robust basis for subsequent studies.