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Geometric Function Theory: A Second Course in Complex Analysis(Springer Undergraduate Mathematics Series)

Geometric Function Theory: A Second Course in Complex Analysis(Springer Undergraduate Mathematics Series)

          
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About the Book

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.

Table of Contents:
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.


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Product Details
  • ISBN-13: 9783031737268
  • Publisher: Springer International Publishing AG
  • Publisher Imprint: Springer International Publishing AG
  • Height: 235 mm
  • No of Pages: 353
  • Series Title: Springer Undergraduate Mathematics Series
  • Width: 155 mm
  • ISBN-10: 3031737261
  • Publisher Date: 13 Dec 2024
  • Binding: Paperback
  • Language: English
  • Returnable: Y
  • Sub Title: A Second Course in Complex Analysis


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Geometric Function Theory: A Second Course in Complex Analysis(Springer Undergraduate Mathematics Series)
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Geometric Function Theory: A Second Course in Complex Analysis(Springer Undergraduate Mathematics Series)
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