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Geometric function theory = a second course in complex analysis /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric function theory/ by Tom Carroll.
其他題名:	a second course in complex analysis /
作者:	Carroll, Tom.
出版者:	Cham :Springer Nature Switzerland : : 2024.,
面頁冊數:	xi, 353 p. :ill. (chiefly color), digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Geometric function theory. -
電子資源:	https://doi.org/10.1007/978-3-031-73727-5
ISBN:	9783031737275

Geometric function theory = a second course in complex analysis /
Carroll, Tom.

Geometric function theorya second course in complex analysis /[electronic resource] :by Tom Carroll. - Cham :Springer Nature Switzerland :2024. - xi, 353 p. :ill. (chiefly color), digital ;24 cm. - Springer undergraduate mathematics series,2197-4144. - Springer undergraduate mathematics series..

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.

ISBN: 9783031737275

Standard No.: 10.1007/978-3-031-73727-5doiSubjects--Topical Terms:

606084
Geometric function theory.

LC Class. No.: QA360

Dewey Class. No.: 515.9

Geometric function theory = a second course in complex analysis /
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505 0 $a 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.
520 $a 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.
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