03395nam a22004815i 4500 978-3-031-54831-4 DE-He213 20251030111824.0 cr nn 008mamaa 240418s2024 sz | s |||| 0|eng d 9783031548314 978-3-031-54831-4 10.1007/978-3-031-54831-4 doi QA299.6-433 PBK bicssc MAT034000 bisacsh PBK thema Aksoy, Asuman Güven. author. aut http://id.loc.gov/vocabulary/relators/aut 75367 Fundamentals of Real and Complex Analysis [electronic resource] / by Asuman Güven Aksoy. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XIV, 394 p. 126 illus., 8 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Undergraduate Mathematics Series, 2197-4144 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. Mathematical analysis. 64178 Analysis. SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031548307 Printed edition: 9783031548321 Springer Undergraduate Mathematics Series, 2197-4144 75368 https://doi.org/10.1007/978-3-031-54831-4 ZDB-2-SMA ZDB-2-SXMS 59208 59208