Complex analysis
Author(s)
Bibliographic Information
Complex analysis
（Undergraduate texts in mathematics）
Springer, c2001
- : hc
- : softcover
Available at / 66 libraries
-
Kyoto Institute of Technology Library図
: hc413.52||G189200311193,
: softcover413.52||G189200402821 -
Hiroshima University Central Library, Interlibrary Loan
: hc413:G-18/HL4010004000410730,
: softcover413:G-18/HL2135102030411263 -
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Note
Bibliography: p. 469
Includes index
Description and Table of Contents
Description
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.
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
by "Nielsen BookData"
