03357nam a22005055i 4500 978-3-031-73727-5 DE-He213 20251030114614.0 cr nn 008mamaa 241212s2024 sz | s |||| 0|eng d 9783031737275 978-3-031-73727-5 10.1007/978-3-031-73727-5 doi QA331.7 PBKD bicssc MAT040000 bisacsh PBKD thema Carroll, Tom. author. (orcid)0000-0002-5450-2490 https://orcid.org/0000-0002-5450-2490 aut http://id.loc.gov/vocabulary/relators/aut 88819 Geometric Function Theory [electronic resource] : A Second Course in Complex Analysis / by Tom Carroll. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XI, 353 p. 67 illus., 55 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 1 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. This 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. Functions of complex variables. 72222 Geometry, Hyperbolic. 80110 Functions of a Complex Variable. 72224 Hyperbolic Geometry. 80111 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031737268 Printed edition: 9783031737282 Springer Undergraduate Mathematics Series, 2197-4144 75368 https://doi.org/10.1007/978-3-031-73727-5 ZDB-2-SMA ZDB-2-SXMS 65647 65647