Modern Methods In Complex Analysis

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Modern Methods in Complex Analysis (AM-137), Volume 137

Author : Thomas Bloom
Publisher : Princeton University Press
ISBN 13 : 1400882575
Total Pages : 360 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Modern Methods in Complex Analysis (AM-137), Volume 137 by : Thomas Bloom

Download or read book Modern Methods in Complex Analysis (AM-137), Volume 137 written by Thomas Bloom and published by Princeton University Press. This book was released on 2016-03-02 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field. The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.

Modern Methods in Complex Analysis

Author : Thomas Bloom
Publisher : Princeton University Press
ISBN 13 : 9780691044286
Total Pages : 366 pages
Book Rating : 4.0/5 (442 download)

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Book Synopsis Modern Methods in Complex Analysis by : Thomas Bloom

Download or read book Modern Methods in Complex Analysis written by Thomas Bloom and published by Princeton University Press. This book was released on 1995-12-03 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well-known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well-presented introduction to the most recent important developments in the field. The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.

Complex Analysis

Author : Theodore W. Gamelin
Publisher : Springer Science & Business Media
ISBN 13 : 0387216073
Total Pages : 508 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Complex Analysis by : Theodore W. Gamelin

Download or read book Complex Analysis written by Theodore W. Gamelin and published by Springer Science & Business Media. This book was released on 2013-11-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Visual Complex Analysis

Author : Tristan Needham
Publisher : Oxford University Press
ISBN 13 : 9780198534464
Total Pages : 620 pages
Book Rating : 4.5/5 (344 download)

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Book Synopsis Visual Complex Analysis by : Tristan Needham

Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Analysis

Author : Jerry R. Muir, Jr.
Publisher : John Wiley & Sons
ISBN 13 : 1118705270
Total Pages : 274 pages
Book Rating : 4.1/5 (187 download)

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Book Synopsis Complex Analysis by : Jerry R. Muir, Jr.

Download or read book Complex Analysis written by Jerry R. Muir, Jr. and published by John Wiley & Sons. This book was released on 2015-05-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem. Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features: Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects Numerous figures to illustrate geometric concepts and constructions used in proofs Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes Appendices on the basics of sets and functions and a handful of useful results from advanced calculus Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.

An Introduction to Complex Analysis

Author : Wolfgang Tutschke
Publisher : CRC Press
ISBN 13 : 1420057219
Total Pages : 476 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis An Introduction to Complex Analysis by : Wolfgang Tutschke

Download or read book An Introduction to Complex Analysis written by Wolfgang Tutschke and published by CRC Press. This book was released on 2004-06-25 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Like real analysis, complex analysis has generated methods indispensable to mathematics and its applications. Exploring the interactions between these two branches, this book uses the results of real analysis to lay the foundations of complex analysis and presents a unified structure of mathematical analysis as a whole. To set the groundwork

A Course of Modern Analysis

Author : E. T. Whittaker
Publisher : Cambridge University Press
ISBN 13 : 1009008595
Total Pages : 722 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis A Course of Modern Analysis by : E. T. Whittaker

Download or read book A Course of Modern Analysis written by E. T. Whittaker and published by Cambridge University Press. This book was released on 2021-08-26 with total page 722 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work has been a unique resource for thousands of mathematicians, scientists and engineers since its first appearance in 1902. Never out of print, its continuing value lies in its thorough and exhaustive treatment of special functions of mathematical physics and the analysis of differential equations from which they emerge. The book also is of historical value as it was the first book in English to introduce the then modern methods of complex analysis. This fifth edition preserves the style and content of the original, but it has been supplemented with more recent results and references where appropriate. All the formulas have been checked and many corrections made. A complete bibliographical search has been conducted to present the references in modern form for ease of use. A new foreword by Professor S.J. Patterson sketches the circumstances of the book's genesis and explains the reasons for its longevity. A welcome addition to any mathematician's bookshelf, this will allow a whole new generation to experience the beauty contained in this text.

Concise Complex Analysis

Author : Sheng Gong
Publisher : World Scientific
ISBN 13 : 9812706933
Total Pages : 258 pages
Book Rating : 4.8/5 (127 download)

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Book Synopsis Concise Complex Analysis by : Sheng Gong

Download or read book Concise Complex Analysis written by Sheng Gong and published by World Scientific. This book was released on 2007 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is a concise textbook of complex analysis for undergraduate and graduate students. Written from the viewpoint of modern mathematics - the d-equation, differential geometry, Lie group, etc. it contains all the traditional material on complex analysis. However, many statement and proofs of classical theorems in complex analysis have been made simpler, shorter and more elegant due to modern mathematical ideas and methods. For example, the Mittag-Leffer theorem is proved by the d-equation, the Picard theorem is proved using the methods of differential geometry, and so on."--BOOK JACKET.

Complex Analysis – Methods, Trends, and Applications

Author : Eberhard Lanckau
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3112707753
Total Pages : 400 pages
Book Rating : 4.1/5 (127 download)

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Book Synopsis Complex Analysis – Methods, Trends, and Applications by : Eberhard Lanckau

Download or read book Complex Analysis – Methods, Trends, and Applications written by Eberhard Lanckau and published by Walter de Gruyter GmbH & Co KG. This book was released on 1983-12-31 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Complex Analysis – Methods, Trends, and Applications".

Complex Analysis

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Complex Analysis by : Elias M. Stein

Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Complex Analysis in Number Theory

Author : Anatoly A. Karatsuba
Publisher : CRC Press
ISBN 13 : 9780849328664
Total Pages : 218 pages
Book Rating : 4.3/5 (286 download)

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Book Synopsis Complex Analysis in Number Theory by : Anatoly A. Karatsuba

Download or read book Complex Analysis in Number Theory written by Anatoly A. Karatsuba and published by CRC Press. This book was released on 1994-11-22 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book examines the application of complex analysis methods to the theory of prime numbers. In an easy to understand manner, a connection is established between arithmetic problems and those of zero distribution for special functions. Main achievements in this field of mathematics are described. Indicated is a connection between the famous Riemann zeta-function and the structure of the universe, information theory, and quantum mechanics. The theory of Riemann zeta-function and, specifically, distribution of its zeros are presented in a concise and comprehensive way. The full proofs of some modern theorems are given. Significant methods of the analysis are also demonstrated as applied to fundamental problems of number theory.

Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations

Author : A S A Mshimba
Publisher : World Scientific
ISBN 13 : 9814548537
Total Pages : 442 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations by : A S A Mshimba

Download or read book Functional Analytic Methods In Complex Analysis And Applications To Partial Differential Equations written by A S A Mshimba and published by World Scientific. This book was released on 1995-10-17 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings concentrate on recent results in the following fields of complex analysis: complex methods for solving boundary value problems with piecewise smooth boundary data, complex methods for linear and nonlinear differential equations and systems of second order, and applications of scales of Banach spaces to initial value problems.Some problems in higher dimensions (such as the unification of global and local existence theorems for holomorphic functions and an elementary approach to Clifford analysis) are also discussed.Particular emphasis is placed on Symbolic Computation in Complex Analysis and on the new approaches to teach mathematical analysis based on interactions between complex analysis and partial differential equations.

Introductory Complex Analysis

Author : Richard A. Silverman
Publisher : Courier Corporation
ISBN 13 : 0486318524
Total Pages : 402 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Introductory Complex Analysis by : Richard A. Silverman

Download or read book Introductory Complex Analysis written by Richard A. Silverman and published by Courier Corporation. This book was released on 2013-04-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Complex Analysis

Author : Jane P. Gilman
Publisher : Springer Science & Business Media
ISBN 13 : 038774715X
Total Pages : 230 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Complex Analysis by : Jane P. Gilman

Download or read book Complex Analysis written by Jane P. Gilman and published by Springer Science & Business Media. This book was released on 2007-11-25 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors’ aim here is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician. They follow a path in the tradition of Ahlfors and Bers by dedicating the book to a very precise goal: the statement and proof of the Fundamental Theorem for functions of one complex variable. They discuss the many equivalent ways of understanding the concept of analyticity, and offer a leisure exploration of interesting consequences and applications. Readers should have had undergraduate courses in advanced calculus, linear algebra, and some abstract algebra. No background in complex analysis is required.

Complex Analysis with Applications in Science and Engineering

Author : Harold Cohen
Publisher : Springer Science & Business Media
ISBN 13 : 0387730583
Total Pages : 487 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Complex Analysis with Applications in Science and Engineering by : Harold Cohen

Download or read book Complex Analysis with Applications in Science and Engineering written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2010-04-23 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this acclaimed text helps you apply theory to real-world applications in mathematics, physics, and engineering. It easily guides you through complex analysis with its excellent coverage of topics such as series, residues, and the evaluation of integrals; multi-valued functions; conformal mapping; dispersion relations; and analytic continuation. Worked examples plus a large number of assigned problems help you understand how to apply complex concepts and build your own skills by putting them into practice. This edition features many new problems, revised sections, and an entirely new chapter on analytic continuation.

Complex Analysis and Special Topics in Harmonic Analysis

Author : Carlos A. Berenstein
Publisher : Springer Science & Business Media
ISBN 13 : 1461384451
Total Pages : 491 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Complex Analysis and Special Topics in Harmonic Analysis by : Carlos A. Berenstein

Download or read book Complex Analysis and Special Topics in Harmonic Analysis written by Carlos A. Berenstein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: A companion volume to the text "Complex Variables: An Introduction" by the same authors, this book further develops the theory, continuing to emphasize the role that the Cauchy-Riemann equation plays in modern complex analysis. Topics considered include: Boundary values of holomorphic functions in the sense of distributions; interpolation problems and ideal theory in algebras of entire functions with growth conditions; exponential polynomials; the G transform and the unifying role it plays in complex analysis and transcendental number theory; summation methods; and the theorem of L. Schwarz concerning the solutions of a homogeneous convolution equation on the real line and its applications in harmonic function theory.

Complex Analytic Sets

Author : E.M. Chirka
Publisher : Springer Science & Business Media
ISBN 13 : 940092366X
Total Pages : 386 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Complex Analytic Sets by : E.M. Chirka

Download or read book Complex Analytic Sets written by E.M. Chirka and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of complex analytic sets is part of the modern geometrical theory of functions of several complex variables. A wide circle of problems in multidimensional complex analysis, related to holomorphic functions and maps, can be reformulated in terms of analytic sets. In these reformulations additional phenomena may emerge, while for the proofs new methods are necessary. (As an example we can mention the boundary properties of conformal maps of domains in the plane, which may be studied by means of the boundary properties of the graphs of such maps.) The theory of complex analytic sets is a relatively young branch of complex analysis. Basically, it was developed to fulfill the need of the theory of functions of several complex variables, but for a long time its development was, so to speak, within the framework of algebraic geometry - by analogy with algebraic sets. And although at present the basic methods of the theory of analytic sets are related with analysis and geometry, the foundations of the theory are expounded in the purely algebraic language of ideals in commutative algebras. In the present book I have tried to eliminate this noncorrespondence and to give a geometric exposition of the foundations of the theory of complex analytic sets, using only classical complex analysis and a minimum of algebra (well-known properties of polynomials of one variable). Moreover, it must of course be taken into consideration that algebraic geometry is one of the most important domains of application of the theory of analytic sets, and hence a lot of attention is given in the present book to algebraic sets.