Lectures on the Theory of Functions of a Complex Variable: Holomorphic functions
Author | : Giovanni Sansone |
Publisher | : |
Total Pages | : 506 |
Release | : 1960 |
Genre | : Functions of complex variables |
ISBN | : |
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Author | : Giovanni Sansone |
Publisher | : |
Total Pages | : 506 |
Release | : 1960 |
Genre | : Functions of complex variables |
ISBN | : |
Author | : Vladimir Ivanovich Smirnov |
Publisher | : |
Total Pages | : 522 |
Release | : 1968 |
Genre | : Functions of complex variables |
ISBN | : |
Author | : Gennadiĭ Mikhaĭlovich Goluzin |
Publisher | : American Mathematical Soc. |
Total Pages | : 690 |
Release | : 1969 |
Genre | : Functions of complex variables |
ISBN | : 9780821886557 |
Author | : Giovanni Sansone |
Publisher | : |
Total Pages | : 508 |
Release | : 1960 |
Genre | : Functions of complex variables |
ISBN | : |
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 | : Elias M. Stein |
Publisher | : Princeton University Press |
Total Pages | : 398 |
Release | : 2010-04-22 |
Genre | : Mathematics |
ISBN | : 1400831156 |
With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.
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 | : Tristan Needham |
Publisher | : Oxford University Press |
Total Pages | : 620 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780198534464 |
This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.
Author | : Raghavan Narasimhan |
Publisher | : University of Chicago Press |
Total Pages | : 185 |
Release | : 1971 |
Genre | : Mathematics |
ISBN | : 0226568172 |
Drawn from lectures given by Raghavan Narasimhan at the University of Geneva and the University of Chicago, this book presents the part of the theory of several complex variables pertaining to unramified domains over C . Topics discussed are Hartogs' theory, domains in holomorphy, and automorphism of bounded domains.