Undergraduate Texts in Mathematics Ser.: Complex Analysis by Theodore W. Gamelin (2001, Hardcover)

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Complex Analysis (Undergraduate Texts in Mathematics) by Gamelin (hardcover).

About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387950931

ISBN-139780387950938

eBay Product ID (ePID)1844178

Product Key Features

Number of PagesXviii, 480 Pages

LanguageEnglish

Publication NameComplex Analysis

SubjectGeneral, Mathematical Analysis

Publication Year2001

TypeTextbook

AuthorTheodore W. Gamelin

Subject AreaMathematics

SeriesUndergraduate Texts in Mathematics Ser.

FormatHardcover

Dimensions

Item Weight32.1 Oz

Item Length9.3 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN00-041905

Dewey Edition21

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal515

Table Of ContentFirst 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.

SynopsisThe book provides an introduction to complex analysis for students withsome familiarity with complex numbers from high school. The bookconsists of three parts. The first part comprises the basic core of acourse in complex analysis for junior and senior undergraduates. Thesecond part includes various more specialized topics as the argumentprinciple, the Schwarz lemma and hyperbolic geometry, the Poissonintegral, and the Riemann mapping theorem. The third part consists ofa selection of topics designed to complete the coverage of allbackground necessary for passing PhD qualifying exams in complexanalysis. Topics selected include Julia sets and the Mandelbrot set,Dirichlet series and the prime number theorem, and the uniformizationtheorem for Riemann surfaces. The three geometries, spherical,euclidean, and hyperbolic, are stressed. Exercises range from the verysimple to the quite challenging, in all chapters. The book is based onlectures given over the years by the author at several places,particularly the Interuniversity Summer School at Perugia (Italy), andalso UCLA, Brown University, Valencia (Spain), and La Plata(Argentina).A native of Minnesota, the author did his undergraduate work at YaleUniversity and his graduate work at UC Berkeley. After spending sometime at MIT and at the Universidad Nacional de La Plata (Argentina), hejoined the faculty at UCLA in 1968. The author has published a numberof research articles and several books on functional analysis andanalytic function theory. he is currently involved in the CaliforniaK-12 education scene., 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., 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., 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.

LC Classification NumberQA299.6-433