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Table of contents:
The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. The book consists of three parts. The first part comprises the basic core of a course in complex analysis for junior and senior undergraduates. The second part includes various more specialized topics such as the argument principle, the Schwarz lemma and hyperbolic geometry, the Poisson integral, and the Riemann mapping theorem. The third part consists of a selection of topics designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics selected 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, particularly the Interuniversity Summer School at Perugia (Italy), and also UCLA, Brown University, Valencia (Spain), and La Plata (Argentina). A native of Minnesota, the author did his undergraduate work at Yale University and his graduate work at UC Berkeley. After spending some time at MIT and at the Universidad Nacional de La Plata (Argentina), he joined the faculty at UCLA in 1968.
Contents:
The Complex Plane and Elementary Functions.- Analytic Functions.- Line Integrals and Harmonic Functions.- Complex Integration and Analyticity.- Power Series.- Laurent Series and Isolated Singularities.- The Residue Calculus.- The Logarithmic Integral.- The Schwarz Lemma and Hyperbolic Geometry.- Harmonic Functions and the Reflection Principle.- Conformal Mapping.- Compact Families of Meromorphic Functions.- Approximation Theorems.- Some Special Functions.- The Dirichlet Problem.- Riemann Surfaces.
Brief Description:
Offers an introduction to complex analysis for students with some familiarity with complex numbers from high school. This book covers the basic core of a course in complex analysis for junior and senior undergraduates, includes various topics as the argument principle, and offers a selection of topics which help in passing PhD qualifying exams.
For Pricing and Availability Click Here
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