The Theory of Functions of Real Variables

Author: Lawrence M Graves
Publisher: Courier Corporation
ISBN: 0486158136
Format: PDF, ePub, Mobi
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This balanced introduction covers all fundamentals, from the real number system and point sets to set theory and metric spaces. Useful references to the literature conclude each chapter. 1956 edition.

Methods of the Theory of Functions of Many Complex Variables

Author: Vasiliy Sergeyevich Vladimirov
Publisher: Courier Corporation
ISBN: 0486458121
Format: PDF, Docs
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This systematic exposition outlines the fundamentals of the theory of single sheeted domains of holomorphy. It further illustrates applications to quantum field theory, the theory of functions, and differential equations with constant coefficients. Students of quantum field theory will find this text of particular value. The text begins with an introduction that defines the basic concepts and elementary propositions, along with the more salient facts from the theory of functions of real variables and the theory of generalized functions. Subsequent chapters address the theory of plurisubharmonic functions and pseudoconvex domains, along with characteristics of domains of holomorphy. These explorations are further examined in terms of four types of domains: multiple-circular, tubular, semitubular, and Hartogs' domains. Surveys of integral representations focus on the Martinelli-Bochner, Bergman-Weil, and Bochner representations. The final chapter is devoted to applications, particularly those involved in field theory. It employs the theory of generalized functions, along with the theory of functions of several complex variables.

Theory of Functions of a Real Variable

Author: I.P. Natanson
Publisher: Courier Dover Publications
ISBN: 048680643X
Format: PDF, Kindle
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Long out-of-print volume by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics. 1955 and 1960 editions.

Real Variables with Basic Metric Space Topology

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486151492
Format: PDF, ePub, Docs
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Designed for a first course in real variables, this text encourages intuitive thinking and features detailed solutions to problems. Topics include complex variables, measure theory, differential equations, functional analysis, probability. 1993 edition.

Applied Complex Variables

Author: John W. Dettman
Publisher: Courier Corporation
ISBN: 0486158284
Format: PDF, ePub, Docs
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Fundamentals of analytic function theory — plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.

Complex Variables

Author: Robert B. Ash
Publisher: Academic Press
ISBN: 1483216195
Format: PDF, ePub
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Complex Variables deals with complex variables and covers topics ranging from Cauchy's theorem to entire functions, families of analytic functions, and the prime number theorem. Major applications of the basic principles, such as residue theory, the Poisson integral, and analytic continuation are given. Comprised of seven chapters, this book begins with an introduction to the basic definitions and concepts in complex variables such as the extended plane, analytic and elementary functions, and Cauchy-Riemann equations. The first chapter defines the integral of a complex function on a path in the complex plane and develops the machinery to prove an elementary version of Cauchy's theorem. Some applications, including the basic properties of power series, are then presented. Subsequent chapters focus on the general Cauchy theorem and its applications; entire functions; families of analytic functions; and the prime number theorem. The geometric intuition underlying the concept of winding number is emphasized. The linear space viewpoint is also discussed, along with analytic number theory, residue theory, and the Poisson integral. This book is intended primarily for students who are just beginning their professional training in mathematics.

Complex Variables

Author: Stephen D. Fisher
Publisher: Courier Corporation
ISBN: 0486406792
Format: PDF, Kindle
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Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.