Applied Complex Variables

Author: John W. Dettman
Publisher: Courier Corporation
ISBN: 0486158284
Format: PDF
Download Now
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.

Fourier Analysis in Several Complex Variables

Author: Leon Ehrenpreis
Publisher: Courier Corporation
ISBN: 0486153037
Format: PDF, Kindle
Download Now
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations. 1970 edition.

Methods of the Theory of Functions of Many Complex Variables

Author: Vasiliy Sergeyevich Vladimirov
Publisher: Courier Corporation
ISBN: 0486458121
Format: PDF, ePub
Download Now
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.

Complex Variable Methods in Elasticity

Author: A. H. England
Publisher: Courier Corporation
ISBN: 048615341X
Format: PDF, Mobi
Download Now
Plane strain and generalized plane stress boundary value problems of linear elasticity are discussed as well as functions of a complex variable, basic equations of 2-dimensional elasticity, plane and half-plane problems, more. 1971 edition. Includes 26 figures.

Complex Variables for Scientists and Engineers

Author: John D. Paliouras
Publisher: Courier Corporation
ISBN: 0486493474
Format: PDF, Mobi
Download Now
Outstanding undergraduate text provides a thorough understanding of fundamentals and creates the basis for higher-level courses. Numerous examples and extensive exercise sections of varying difficulty, plus answers to selected exercises. 1990 edition.

Complex Variables and the Laplace Transform for Engineers

Author: Wilbur R. LePage
Publisher: Courier Corporation
ISBN: 0486136442
Format: PDF, ePub, Mobi
Download Now
Acclaimed text on engineering math for graduate students covers theory of complex variables, Cauchy-Riemann equations, Fourier and Laplace transform theory, Z-transform, and much more. Many excellent problems.

Complex Variables

Author: Robert B. Ash
Publisher: Courier Corporation
ISBN: 0486462501
Format: PDF, Kindle
Download Now
This text on complex variables is geared toward graduate students and undergraduates who have taken an introductory course in real analysis. It is a substantially revised and updated edition of the popular text by Robert B. Ash, offering a concise treatment that provides careful and complete explanations as well as numerous problems and solutions. An introduction presents basic definitions, covering topology of the plane, analytic functions, real-differentiability and the Cauchy-Riemann equations, and exponential and harmonic functions. Succeeding chapters examine the elementary theory and the general Cauchy theorem and its applications, including singularities, residue theory, the open mapping theorem for analytic functions, linear fractional transformations, conformal mapping, and analytic mappings of one disk to another. The Riemann mapping theorem receives a thorough treatment, along with factorization of analytic functions. As an application of many of the ideas and results appearing in earlier chapters, the text ends with a proof of the prime number theorem.

Complex Variables

Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1420010956
Format: PDF
Download Now
From the algebraic properties of a complete number field, to the analytic properties imposed by the Cauchy integral formula, to the geometric qualities originating from conformality, Complex Variables: A Physical Approach with Applications and MATLAB explores all facets of this subject, with particular emphasis on using theory in practice. The first five chapters encompass the core material of the book. These chapters cover fundamental concepts, holomorphic and harmonic functions, Cauchy theory and its applications, and isolated singularities. Subsequent chapters discuss the argument principle, geometric theory, and conformal mapping, followed by a more advanced discussion of harmonic functions. The author also presents a detailed glimpse of how complex variables are used in the real world, with chapters on Fourier and Laplace transforms as well as partial differential equations and boundary value problems. The final chapter explores computer tools, including Mathematica®, MapleTM, and MATLAB®, that can be employed to study complex variables. Each chapter contains physical applications drawing from the areas of physics and engineering. Offering new directions for further learning, this text provides modern students with a powerful toolkit for future work in the mathematical sciences.

Introductory Complex Analysis

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486318524
Format: PDF, Kindle
Download Now
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.