LEADER 03370nam 22005895 450 001 9910917784003321 005 20250527190430.0 010 $a9783031737275$b(electronic bk.) 010 $z9783031737268 024 7 $a10.1007/978-3-031-73727-5 035 $a(MiAaPQ)EBC31827036 035 $a(Au-PeEL)EBL31827036 035 $a(CKB)36976065700041 035 $a(DE-He213)978-3-031-73727-5 035 $a(OCoLC)1481785586 035 $a(EXLCZ)9936976065700041 100 $a20241212d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aGeometric Function Theory $eA Second Course in Complex Analysis /$fby Tom Carroll 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024 215 $a1 online resource (358 pages) 225 1 $aSpringer Undergraduate Mathematics Series,$x2197-4144 311 08$aPrint version: Carroll, Tom Geometric Function Theory Cham : Springer,c2025 9783031737268 327 $a1 Introduction -- 2 The Complex Plane - Preparatory Topics -- 3 The Riemann Sphere -- 4 The Hyperbolic Disk -- 5 Normal Families and Value Distribution -- 6 Simply Connected Domains and the Riemann Mapping Theorem -- 7 Runge's Theorem and Further Characterisations of Simply Connected Domains -- 8 Univalent Functions - the Basics -- 9 Carathéodory Convergence of Domains and Hyperbolic Geodesics -- 10 Uniformisation of Planar Domains. 330 $aThis textbook provides a second course in complex analysis with a focus on geometric aspects. It covers topics such as the spherical geometry of the extended complex plane, the hyperbolic geometry of the Poincaré disk, conformal mappings, the Riemann Mapping Theorem and uniformisation of planar domains, characterisations of simply connected domains, the convergence of Riemann maps in terms of Carathéodory convergence of the image domains, normal families and Picard's theorems on value distribution, as well as the fundamentals of univalent function theory. Throughout the text, the synergy between analysis and geometry is emphasised, with proofs chosen for their directness. The textbook is self-contained, requiring only a first undergraduate course in complex analysis. The minimal topology needed is introduced as necessary. While primarily aimed at upper-level undergraduates, the book also serves as a concise reference for graduates working in complex analysis. 410 0$aSpringer Undergraduate Mathematics Series,$x2197-4144 606 $aFunctions of complex variables 606 $aGeometry, Hyperbolic 606 $aTeoria geomètrica de funcions$2thub 606 $aGeometria hiperbòlica$2thub 606 $aFunctions of a Complex Variable 606 $aHyperbolic Geometry 608 $aLlibres electrònics$2thub 615 0$aFunctions of complex variables. 615 0$aGeometry, Hyperbolic. 615 7$aTeoria geomètrica de funcions 615 7$aGeometria hiperbòlica 615 14$aFunctions of a Complex Variable. 615 24$aHyperbolic Geometry. 676 $a515.9 700 $aCarroll$b Tom$01780012 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a9910917784003321 996 $aGeometric Function Theory$94303670 997 $aUNINA