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Fundamentals of real and complex analysis

Record Type:	Electronic resources : Monograph/item
Title/Author:	Fundamentals of real and complex analysis/ by Asuman Guven Aksoy.
Author:	Aksoy, Asuman G.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xiv, 394 p. :ill. (some col.), digital ;24 cm.
[NT 15003449]:	Preface -- Introductory Analysis -- Real Analysis -- Complex Analysis -- Bibliography -- Index.
Contained By:	Springer Nature eBook
Subject:	Mathematical analysis. -
Online resource:	https://doi.org/10.1007/978-3-031-54831-4
ISBN:	9783031548314

Fundamentals of real and complex analysis
Aksoy, Asuman G.

Fundamentals of real and complex analysis[electronic resource] /by Asuman Guven Aksoy. - Cham :Springer Nature Switzerland :2024. - xiv, 394 p. :ill. (some col.), digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

Preface -- Introductory Analysis -- Real Analysis -- Complex Analysis -- Bibliography -- Index.

The primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science. Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter's unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy's theorem through the integral formula and residue theorem are presented.

ISBN: 9783031548314

Standard No.: 10.1007/978-3-031-54831-4doiSubjects--Topical Terms:

516833
Mathematical analysis.

LC Class. No.: QA300

Dewey Class. No.: 515

Fundamentals of real and complex analysis
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245 1 0 $a Fundamentals of real and complex analysis $h [electronic resource] / $c by Asuman Guven Aksoy.
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490 1 $a Springer undergraduate mathematics series, $x 2197-4144
505 0 $a Preface -- Introductory Analysis -- Real Analysis -- Complex Analysis -- Bibliography -- Index.
520 $a The primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science. Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter's unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy's theorem through the integral formula and residue theorem are presented.
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