000 03357nam a22005055i 4500
001 978-3-031-73727-5
003 DE-He213
005 20251030114614.0
007 cr nn 008mamaa
008 241212s2024 sz | s |||| 0|eng d
020 _a9783031737275
_9978-3-031-73727-5
024 7 _a10.1007/978-3-031-73727-5
_2doi
050 4 _aQA331.7
072 7 _aPBKD
_2bicssc
072 7 _aMAT040000
_2bisacsh
072 7 _aPBKD
_2thema
100 1 _aCarroll, Tom.
_eauthor.
_0(orcid)0000-0002-5450-2490
_1https://orcid.org/0000-0002-5450-2490
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_988819
245 1 0 _aGeometric Function Theory
_h[electronic resource] :
_bA Second Course in Complex Analysis /
_cby Tom Carroll.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer Nature Switzerland :
_bImprint: Springer,
_c2024.
300 _aXI, 353 p. 67 illus., 55 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Undergraduate Mathematics Series,
_x2197-4144
505 0 _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.
520 _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.
650 0 _aFunctions of complex variables.
_972222
650 0 _aGeometry, Hyperbolic.
_980110
650 1 4 _aFunctions of a Complex Variable.
_972224
650 2 4 _aHyperbolic Geometry.
_980111
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031737268
776 0 8 _iPrinted edition:
_z9783031737282
830 0 _aSpringer Undergraduate Mathematics Series,
_x2197-4144
_975368
856 4 0 _uhttps://doi.org/10.1007/978-3-031-73727-5
912 _aZDB-2-SMA
912 _aZDB-2-SXMS
999 _c65647
_d65647