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Complex Analysis and Dynamics in One Variable with Applications
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This textbook has been designed to support the initial study of Complex Analysis, progressing into Complex Dynamics. It focuses on the fundamental aspects of one-variable complex functions, covering the geometric theory and dynamics of iterations of rational functions. Following the standard material, the book delves into an extensive range of advanced topics, encompassing everything required for a one-year graduate-level course or to pass 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, accompanied by several 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, establishing a robust basis for subsequent studies.
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