An Introduction To Complex Function Theory
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| Author | : Bruce P. Palka |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 585 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 038797427X |
This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
| Author | : Donald Sarason |
| Publisher | : American Mathematical Society |
| Total Pages | : 177 |
| Release | : 2021-02-16 |
| Genre | : Mathematics |
| ISBN | : 1470463237 |
Complex Function Theory is a concise and rigorous introduction to the theory of functions of a complex variable. Written in a classical style, it is in the spirit of the books by Ahlfors and by Saks and Zygmund. Being designed for a one-semester course, it is much shorter than many of the standard texts. Sarason covers the basic material through Cauchy's theorem and applications, plus the Riemann mapping theorem. It is suitable for either an introductory graduate course or an undergraduate course for students with adequate preparation. The first edition was published with the title Notes on Complex Function Theory.
| Author | : Robert Everist Greene |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 536 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 9780821839621 |
Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples andexercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem,and the Bergman kernel. The authors also treat $Hp$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.
| Author | : Reinhold Remmert |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 464 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461209390 |
A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.
| Author | : Frank Smithies |
| Publisher | : Cambridge University Press |
| Total Pages | : 242 |
| Release | : 1997-11-20 |
| Genre | : Mathematics |
| ISBN | : 9780521592789 |
Dr Smithies' analysis of the process whereby Cauchy created the basic structure of complex analysis, begins by describing the 18th century background. He then proceeds to examine the stages of Cauchy's own work, culminating in the proof of the residue theorem. Controversies associated with the the birth of the subject are also considered in detail. Throughout, new light is thrown on Cauchy's thinking during this watershed period. This authoritative book is the first to make use of the whole spectrum of available original sources.
| Author | : Henri Cartan |
| Publisher | : Courier Corporation |
| Total Pages | : 242 |
| Release | : 2013-04-22 |
| Genre | : Mathematics |
| ISBN | : 0486318672 |
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
| Author | : Steven George Krantz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 586 |
| Release | : 2001 |
| Genre | : Mathematics |
| ISBN | : 0821827243 |
Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.
| Author | : Murali Rao |
| Publisher | : World Scientific |
| Total Pages | : 254 |
| Release | : 1991 |
| Genre | : Mathematics |
| ISBN | : 9789810203757 |
This is a rigorous introduction to the theory of complex functions of one complex variable. The authors have made an effort to present some of the deeper and more interesting results, for example, Picard's theorems, Riemann mapping theorem, Runge's theorem in the first few chapters. However, the very basic theory is nevertheless given a thorough treatment so that readers should never feel lost. After the first five chapters, the order may be adapted to suit the course. Each chapter finishes with exercises.
| Author | : Theodore W. Gamelin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 508 |
| Release | : 2013-11-01 |
| Genre | : Mathematics |
| ISBN | : 0387216073 |
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.
| Author | : Gareth A. Jones |
| Publisher | : Cambridge University Press |
| Total Pages | : 362 |
| Release | : 1987-03-19 |
| Genre | : Mathematics |
| ISBN | : 9780521313667 |
An elementary account of many aspects of classical complex function theory, including Mobius transformations, elliptic functions, Riemann surfaces, Fuchsian groups and modular functions. The book is based on lectures given to advanced undergraduate students and is well suited as a textbook for a second course in complex function theory.
