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.

�ber die Autorin bzw. den Autor:

Luis T. Magalh�es was a Professor of Mathematics at IST - Instituto Superior T�cnico, University of Lisbon, Portugal, from 1993 to 2001, marking his jubilee. He obtained a degree in Electrical Engineering - Telecommunications and Electronics from IST in 1975, and earned his MSc (1980) and PhD (1982) in Applied Mathematics from Brown University, USA. Dr. Magalh�es has served as President of the Science and Technology Foundation - Portugal, the Knowledge Society Agency - Portugal, the University of Algarve General Council, the INL - International Iberian Nanotechnology Laboratory Council and the INL Installation Committee, chaired the European Union HORIZON 2020 Advisory Board on Research Infrastructures and the OECD Working Party on Measurement and Analysis of the Digital Economy, co-chaired the European Union – Africa Partnership on Science, Information Society and Space, and was a committee or council member in various organizations in Portugal and at European Union, OECD, UN and ICANN. He was the founder and coordinator of a prominent mathematics research center, and a co-founder of the ISR - Institute of Systems and Robotics and Vice-Director of its Lisbon branch. Alongside Jack K. Hale and Waldyr M. Oliva, he co-authored the book "An Introduction to Infinite Dimensional Dynamical Systems," published by Springer. Additionally, he has authored several books in Calculus and Linear Algebra, published in Portuguese.

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Complex Analysis and Dynamics in One Variable with Applications

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