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

Carroll, Tom

Softcover

ISBN 10: 3031737261 ISBN 13: 9783031737268

Publisher: Springer, 2024

Synopsis

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.

About this title

About the Author

Tom Carroll is Senior Lecturer in Mathematics at University College Cork. He is the author of over 40 research papers, primarily in the general areas of functions of a complex variable, probability theory and stochastic processes, and partial differential equations. Tom has served as President of the Irish Mathematical Society (2021-2022) and has recently been appointed editor of the Society's Bulletin.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2024
• Language: English
• ISBN 10: 3031737261
• ISBN 13: 9783031737268
• Binding: Paperback
• Number of pages: 364