Theodore W. Gamelin: Complex Analysis | Buch

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Cover: 9780387950938 | Complex Analysis | Theodore W. Gamelin | Buch | XVIII | Englisch

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Sprache: Englisch

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Beschreibung

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. It conists of sixteen chapters. The first eleven chapters are aimed at an Upper Division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters. The book is based on lectures given over the years by the author at several places, including UCLA, Brown University, the universities at La Plata and Buenos Aires, Argentina; and the Universidad Autonomo de Valencia, Spain.

Über den Autor

Zusammenfassung

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. Topics studied in the book include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces. The three geometries, spherical, euclidean, and hyperbolic, are stressed. Exercises range from the very simple to the quite challenging, in all chapters.

Inhaltsverzeichnis

First Part.- I The Complex Plane and Elementary Functions.- II Analytic Functions.- III Line Integrals and Harmonic Functions.- IV Complex Integration and Analyticity.- V Power Series.- VI Laurent Series and Isolated Singularities.- VII The Residue Calculus.- Second Part.- VIII The Logarithmic Integral.- IX The Schwarz Lemma and Hyperbolic Geometry.- X Harmonic Functions and the Reflection Principle.- XI Conformal Mapping.- Third Part.- XII Compact Families of Meromorphic Functions.- XIII Approximation Theorems.- XIV Some Special Functions.- XV The Dirichlet Problem.- XVI Riemann Surfaces.- Hints and Solutions for Selected Exercises.- References.- List of Symbols.

Erscheinungsjahr:	2001
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Buch
Seiten:	500
Reihe:	Undergraduate Texts in Mathematics
Inhalt:	xviii 480 S.
ISBN-13:	9780387950938
ISBN-10:	0387950931
Sprache:	Englisch
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Gamelin, Theodore W.
Auflage:	2001
Hersteller:	Springer US Springer New York Undergraduate Texts in Mathematics
Maße:	241 x 160 x 33 mm
Von/Mit:	Theodore W. Gamelin
Erscheinungsdatum:	18.05.2001
Gewicht:	0,91 kg

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