Theodore W. Gamelin

Complex Analysis

• Broschiertes Buch

Produktbeschreibung

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.

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Produktdetails

• Undergraduate Texts in Mathematics
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-0-387-95069-3
• 1st ed. 2001 corr. 2nd printing 2001
• Seitenzahl: 500
• Erscheinungstermin: 18. Mai 2001
• Englisch
• Abmessung: 235mm x 155mm x 27mm
• Gewicht: 780g
• ISBN-13: 9780387950693
• ISBN-10: 0387950699
• Artikelnr.: 09304308

Autorenporträt

Inhaltsangabe

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.

Rezensionen

More than 800 well-chosen exercises with 20 pages of hints and solutions, together with clear and concise expositions of many results, makes this book enjoyable even for specialists in the field. The book is recommended for libraries, students, and teachers of both undergraduate and graduate courses. Newsletter of the EMS, Issue 42, December.