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Complex Analysis

Author: Jerry R. Muir
Publisher: John Wiley & Sons
ISBN: 111870522X
Size: 38.49 MB
Format: PDF, ePub
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This book concisely addresses the classical results of the field, emphasizes the beauty, power, and counterintuitive nature of the subject, and moves the notion of power series front and center, giving readers a primary tool to deal with problems from modern function theory. Uniquely defines analyticity in terms of power series (as opposed to differentiability), making power series a central concept and tool to solve problems Features many “counterintuitive” concepts as a learning tool, such as addressing Liouville's Theorem, the factorization of analytic function, the Open Mapping Theorem, and the Maximum Principle in quick succession early on in the book in an attempt to prepare readers for the development of the Cauchy integral theory Classroom tested for 10+ years by the author at the University of Scranton as well as colleagues at Rose-Hulman Institute of Technology and Adams State College Presents sequences and series early on, distinguishes complex analysis from real analysis and calculus, and emphasizes geometry when analyzing complex functions Contains appendices for basic notation of sets and functions as well as necessary topics from advanced calculus, such as Leibnitz's Rule and Fubini's Theorem An Instructor's Manual containing all solutions is available via request to the Publisher. Written with a reader-friendly approach and provides a wide range of exercises and numerous figures throughout, allowing readers to gain intuition for solving problems.

Function Theory Of One Complex Variable

Author: Robert Everist Greene
Publisher: American Mathematical Soc.
ISBN: 9780821839621
Size: 21.30 MB
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This book is a text for a first-year graduate course in complex analysis. It is a modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors."--BOOK JACKET.

Complex Analysis

Author: Jane P. Gilman
Publisher: Springer Science & Business Media
ISBN: 0387747141
Size: 70.76 MB
Format: PDF
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Organizing the basic material of complex analysis in a unique manner, the authors of this versatile book aim is to present a precise and concise treatment of those parts of complex analysis that should be familiar to every research mathematician.

Geometric Function Theory

Author: Steven G. Krantz
Publisher: Springer Science & Business Media
ISBN: 0817644407
Size: 39.89 MB
Format: PDF, Docs
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* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Complex Analysis

Author: John Stalker
Publisher: Springer Science & Business Media
ISBN: 0817649182
Size: 27.86 MB
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In this concise introduction to the classical theory of one complex variable the content is driven by techniques and examples, rather than definitions and theorems.

Hidden Harmony Geometric Fantasies

Author: Umberto Bottazzini
Publisher: Springer Science & Business Media
ISBN: 1461457254
Size: 21.20 MB
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​This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and Weierstrass – it looks at the contributions of authors from d’Alembert to Hilbert, and Laplace to Weyl. Particular chapters examine the rise and importance of elliptic function theory, differential equations in the complex domain, geometric function theory, and the early years of complex function theory in several variables. Unique emphasis has been devoted to the creation of a textbook tradition in complex analysis by considering some seventy textbooks in nine different languages. The book is not a mere sequence of disembodied results and theories, but offers a comprehensive picture of the broad cultural and social context in which the main actors lived and worked by paying attention to the rise of mathematical schools and of contrasting national traditions. The book is unrivaled for its breadth and depth, both in the core theory and its implications for other fields of mathematics. It documents the motivations for the early ideas and their gradual refinement into a rigorous theory.​

Geometric Analysis And Function Spaces

Author: Steven George Krantz
Publisher: American Mathematical Soc.
ISBN: 9780821889251
Size: 50.65 MB
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This book brings into focus the synergistic interaction between analysis and geometry by examining a variety of topics in function theory, real analysis, harmonic analysis, several complex variables, and group actions. Krantz's approach is motivated by examples, both classical and modern, which highlight the symbiotic relationship between analysis and geometry. Creating a synthesis among a host of different topics, this book is useful to researchers in geometry and analysis and may be of interest to physicists, astronomers, and engineers in certain areas. The book is based on lectures presented at an NSF-CBMS Regional Conference held in May 1992.

Applied And Computational Complex Analysis Volume 3

Author: Peter Henrici
Publisher: Wiley-Interscience
ISBN: 9780471087038
Size: 17.77 MB
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Presents applications as well as the basic theory of analytic functions of one or several complex variables. The first volume discusses applications and basic theory of conformal mapping and the solution of algebraic and transcendental equations. Volume Two covers topics broadly connected with ordinary differental equations: special functions, integral transforms, asymptotics and continued fractions. Volume Three details discrete fourier analysis, cauchy integrals, construction of conformal maps, univalent functions, potential theory in the plane and polynomial expansions.

Concise Complex Analysis

Author: Sheng Gong
Publisher: World Scientific
ISBN: 9789810243791
Size: 73.51 MB
Format: PDF, Kindle
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This is a concise textbook of complex analysis for undergraduate and graduate students. It has been written from the viewpoint of modern mathematics -- the -equation, differential geometry, Lie groups, etc. It contains all the traditional material on complex analysis, but many statements 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-Leffler theorem is proved by the -equation, the Picard theorem is proved using the methods of differential geometry, and so on.

Advanced Real Analysis

Author: Anthony W. Knapp
Publisher: Springer Science & Business Media
ISBN: 9780817644420
Size: 56.44 MB
Format: PDF, Mobi
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* Presents a comprehensive treatment with a global view of the subject * Rich in examples, problems with hints, and solutions, the book makes a welcome addition to the library of every mathematician