Fundamentals of Real and Complex Analysis von Asuman Güven Aksoy | ISBN 9783031548314

Fundamentals of Real and Complex Analysis

von Asuman Güven Aksoy
Buchcover Fundamentals of Real and Complex Analysis | Asuman Güven Aksoy | EAN 9783031548314 | ISBN 3-031-54831-0 | ISBN 978-3-031-54831-4

“This book is well-suited for advanced undergraduate students seeking a strong foundation in real and complex analysis … . It's a good choice for instructors looking for a textbook that emphasizes both rigour and intuition in analysis. This book is an excellent resource for students of mathematics looking to build a strong understanding of analysis. Its comprehensive coverage, clarity, and rigour make it a valuable addition to any academic library.” (Dorian Guzu, Mathematical Reviews, January, 2025)

Fundamentals of Real and Complex Analysis

von Asuman Güven Aksoy

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.