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Complex analysis and dynamics in one variable with applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Complex analysis and dynamics in one variable with applicationsby Luis T. Magalhães.
Author:	Magalhães, Luis T.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	xxxii, 714 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Functions.
Online resource:	https://doi.org/10.1007/978-3-031-64999-8
ISBN:	9783031649998$q(electronic bk.)

Complex analysis and dynamics in one variable with applications
Magalhães, Luis T.

Complex analysis and dynamics in one variable with applications[electronic resource] /by Luis T. Magalhães. - Cham :Springer Nature Switzerland :2025. - xxxii, 714 p. :ill. (some col.), digital ;24 cm.

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.

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.

ISBN: 9783031649998$q(electronic bk.)

Standard No.: 10.1007/978-3-031-64999-8doiSubjects--Topical Terms:

221438
Functions.

LC Class. No.: QA331

Dewey Class. No.: 515.9

Complex analysis and dynamics in one variable with applications
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505 0 $a 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.
520 $a 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.
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650 2 4 $a Dynamical Systems. $3 913342
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