Complex Analysis and Dynamics in One Variable with Applications
Springer International Publishing (Verlag)
978-3-031-64998-1 (ISBN)
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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.
Luis T. Magalhães was a Professor of Mathematics at IST - Instituto Superior Técnico, 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. Magalhães has served as a president or council member in various organizations, including the Knowledge Society Agency and the Science and Technology Foundation in Portugal, as well as at ICANN, HORIZON 2020, and OECD. 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 numerous other books in Calculus and Linear Algebra, published in Portuguese.
Complex plane.- Functions.- Derivative.- Integral.- Analyticity.- Uni cation of holomorphy cauchy theorem and analyticity.- Global cauchy theorem.- Meromorphic functions.- Harmonic functions.- Conformal regions.- Analytic continuation and riemann surfaces.- Uniformization of riemann surfaces.- Complex dynamics.
| Erscheint lt. Verlag | 20.1.2025 |
|---|---|
| Zusatzinfo | XXX, 741 p. 228 illus., 59 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Analysis | |
| Schlagworte | Analytic Functions • Cauchy Theorem • Complex Analysis • complex functions • Conformal Mappings • Functions • Harmonic Functions • Holomorphic Functions • Holomorphy • Riemann Surfaces |
| ISBN-10 | 3-031-64998-2 / 3031649982 |
| ISBN-13 | 978-3-031-64998-1 / 9783031649981 |
| Zustand | Neuware |
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