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Complex Analysis (01 Edition)

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Complex Analysis (01 Edition) Cover

ISBN13: 9780387950693
ISBN10: 0387950699
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Synopses & Reviews

Publisher Comments:

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 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. The author has published a number of research articles and several books on functional analysis and analytic function theory. he is currently involved in the California K-12 education scene.

Synopsis:

The book provides an introduction to complex analysis for readers with some very basic familiarity with complex numbers. The sixteen chapters begin with the fundamentals at the undergraduate level, finishing with material designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics covered 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.

Synopsis:

An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which 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 include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.

Synopsis:

The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. 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 as the argument principle 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 Ph.D. qualifying exams in complex analysis.

Table of 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

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vuthinhnguyen, February 26, 2007 (view all comments by vuthinhnguyen)
I am very interesting in this field. I hope that this book could give me more knowledge of functions.
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Product Details

ISBN:
9780387950693
Author:
Gamelin, Theodore W.
Publisher:
Springer
Author:
Gamelin, Theodore W.
Author:
Gamelin, T. W.
Location:
New York, NY
Subject:
Calculus
Subject:
Mathematical Analysis
Subject:
Geometry - General
Subject:
Functions of complex variables
Subject:
Mathematics-Analysis General
Subject:
Analysis
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Number:
1
Edition Description:
2001. Corr. 2nd
Series:
Undergraduate Texts in Mathematics
Series Volume:
63, supl. 1
Publication Date:
January 2001
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
496
Dimensions:
235 x 155 mm 1530 gr

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Related Subjects


Reference » Science Reference » General
Science and Mathematics » Mathematics » Analysis General
Science and Mathematics » Mathematics » Applied
Science and Mathematics » Mathematics » Calculus » General
Science and Mathematics » Mathematics » Complex Analysis
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Probability and Statistics » General
Science and Mathematics » Mathematics » Probability and Statistics » Statistics

Complex Analysis (01 Edition) New Trade Paper
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$55.15 In Stock
Product details 496 pages Springer-Verlag - English 9780387950693 Reviews:
"Synopsis" by , The book provides an introduction to complex analysis for readers with some very basic familiarity with complex numbers. The sixteen chapters begin with the fundamentals at the undergraduate level, finishing with material designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics covered 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.
"Synopsis" by , An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which 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 include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.
"Synopsis" by , The book provides an introduction to complex analysis for students with some familiarity with complex numbers from high school. 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 as the argument principle 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 Ph.D. qualifying exams in complex analysis.
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