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Details for:
Aksoy A. Fundamentals of Real and Complex Analysis 2024
aksoy fundamentals real complex analysis 2024
Type:
E-books
Files:
1
Size:
5.8 MB
Uploaded On:
April 23, 2024, 3:24 p.m.
Added By:
andryold1
Seeders:
5
Leechers:
1
Info Hash:
F2F40E7970B4BAB358A510B32465E9197960766F
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Textbook in PDF format 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. Preface Introductory Analysis Set Theory Number Systems Completeness and the Real Number System Sequences and Series Topology of the Real Line Continuous Functions Differentiability on R The Riemann Integral Real Analysis Metric, Normed, and Inner Product Spaces Fixed Point Theorems and Applications Modes of Convergence Approximation by Polynomials Functional Equations Fourier Series Lebesgue Measure and Integration Banach–Tarski Paradox Complex Analysis The Complex Plane Holomorphic Functions Power Series Some Holomorphic Functions Conformal Mappings Integration in the Complex Plane Cauchy's Theorem Cauchy's Formulae Laurent Expansion and Singularities Applications of Cauchy's Residue Theorem The Bieberbach Conjecture About the Author Bibliography Index
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Aksoy A. Fundamentals of Real and Complex Analysis 2024.pdf
5.8 MB
