Complex Analysis and Dynamics in One Variable with Applications
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Product details:
- Edition number 2024
- Publisher Springer
- Date of Publication 26 May 2025
- Number of Volumes 1 pieces, Book
- ISBN 9783031649981
- Binding Hardback
- No. of pages741 pages
- Size 235x155 mm
- Language English
- Illustrations 169 Illustrations, black & white; 59 Illustrations, color 700
Categories
Short description:
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.
MoreLong description:
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.
MoreTable of Contents:
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.
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