LEADER 03237nam 22005295 450 001 9910851981003321 005 20260225123857.0 010 $a3-031-54831-0 024 7 $a10.1007/978-3-031-54831-4 035 $a(MiAaPQ)EBC31288988 035 $a(Au-PeEL)EBL31288988 035 $a(CKB)31548374000041 035 $a(DE-He213)978-3-031-54831-4 035 $a(MiAaPQ)EBC31290776 035 $a(Au-PeEL)EBL31290776 035 $a(EXLCZ)9931548374000041 100 $a20240418d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFundamentals of Real and Complex Analysis /$fby Asuman Güven Aksoy 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (402 pages) 225 1 $aSpringer Undergraduate Mathematics Series,$x2197-4144 311 08$a3-031-54830-2 327 $aPreface -- Introductory Analysis -- Real Analysis -- Complex Analysis -- Bibliography.-Index. 330 $aThe primary aim of this text is to help transition undergraduates to study graduate level mathematics. It unites real and complex analysis after developing the basic techniques and aims at a larger readership than that of similar textbooks that have been published, as fewer mathematical requisites are required. The idea is to present analysis as a whole and emphasize the strong connections between various branches of the field. Ample examples and exercises reinforce concepts, and a helpful bibliography guides those wishing to delve deeper into particular topics. Graduate students who are studying for their qualifying exams in analysis will find use in this text, as well as those looking to advance their mathematical studies or who are moving on to explore another quantitative science. Chapter 1 contains many tools for higher mathematics; its content is easily accessible, though not elementary. Chapter 2 focuses on topics in real analysis such as p-adic completion, Banach Contraction Mapping Theorem and its applications, Fourier series, Lebesgue measure and integration. One of this chapter?s unique features is its treatment of functional equations. Chapter 3 covers the essential topics in complex analysis: it begins with a geometric introduction to the complex plane, then covers holomorphic functions, complex power series, conformal mappings, and the Riemann mapping theorem. In conjunction with the Bieberbach conjecture, the power and applications of Cauchy?s theorem through the integral formula and residue theorem are presented. 410 0$aSpringer Undergraduate Mathematics Series,$x2197-4144 606 $aMathematical analysis 606 $aAnalysis 606 $aAnàlisi matemàtica$2thub 608 $aLlibres electrònics$2thub 615 0$aMathematical analysis. 615 14$aAnalysis. 615 7$aAnàlisi matemàtica 676 $a515 700 $aAksoy$b Asuman Gu?ven$059487 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910851981003321 996 $aFundamentals of Real and Complex Analysis$94236381 997 $aUNINA