03184nam a22004335i 4500001001800000003000900018005001700027007001500044008004100059020003700100024003500137050001600172072001600188072002300204072001500227100009100242245009700333250001800430264006900448300006500517336002600582337002600608338003600634347002400670490005800694505009800752520156300850650003402413650001402447710003402461773002602495776003602521776003602557830006502593856004602658912001402704912001502718999001702733978-3-031-54831-4DE-He21320251030111824.0cr nn 008mamaa240418s2024    sz |    s    |||| 0|eng d  a97830315483149978-3-031-54831-47 a10.1007/978-3-031-54831-42doi 4aQA299.6-433 7aPBK2bicssc 7aMAT0340002bisacsh 7aPBK2thema1 aAksoy, Asuman Güven.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut97536710aFundamentals of Real and Complex Analysish[electronic resource] /cby Asuman Güven Aksoy.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXIV, 394 p. 126 illus., 8 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSpringer Undergraduate Mathematics Series,x2197-41440 aPreface -- Introductory Analysis -- Real Analysis -- Complex Analysis -- Bibliography.-Index.  aThe 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. 0aMathematical analysis.96417814aAnalysis.2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303154830708iPrinted edition:z9783031548321 0aSpringer Undergraduate Mathematics Series,x2197-414497536840uhttps://doi.org/10.1007/978-3-031-54831-4  aZDB-2-SMA  aZDB-2-SXMS  c59208d59208