Complex Variables And Their Applications

Author : Anthony D. Osborne
Publisher : Addison Wesley
Page : 472 pages
File Size : 43,9 Mb
Release : 1999
Category : Mathematics
ISBN : UOM:39015047608891

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Complex Variables and Their Applications by Anthony D. Osborne Pdf

An understanding of functions of a complex variable, together with the importance of their applications, form an essential part of the study of mathematics. Complex Variables and their Applications assumes as little background knowledge of the reader as is practically possible, a sound knowledge of calculus and basic real analysis being the only essential pre-requisites. With an emphasis on clear and careful explanation, the book covers all the essential topics covered in a first course on Complex Variables, such as differentiation, integration and applications, Laurent series, residue theory and applications, and elementary conformal mappings. The reader is also introduced to the Schwarz-Christoffel transformation, Dirchlet problems, harmonic functions, analytic continuation, infinite products, asymptotic series and elliptic functions. Applications of complex variable theory to linear ordinary differential equations and integral transforms are also included. Complex Variables and their Applications is an ideal textbook and resource for second and final year students of mathematics, engineering and physics.

Author : Saminathan Ponnusamy,Herb Silverman
Publisher : Springer Science & Business Media
Page : 514 pages
File Size : 46,8 Mb
Release : 2007-05-26
Category : Mathematics
ISBN : 9780817645137

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Complex Variables with Applications by Saminathan Ponnusamy,Herb Silverman Pdf

Explores the interrelations between real and complex numbers by adopting both generalization and specialization methods to move between them, while simultaneously examining their analytic and geometric characteristics Engaging exposition with discussions, remarks, questions, and exercises to motivate understanding and critical thinking skills Encludes numerous examples and applications relevant to science and engineering students

Author : John W. Dettman
Publisher : Courier Corporation
Page : 512 pages
File Size : 45,8 Mb
Release : 2012-05-07
Category : Mathematics
ISBN : 9780486158280

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Applied Complex Variables by John W. Dettman Pdf

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.

Author : Mark J. Ablowitz,Athanassios S. Fokas
Publisher : Cambridge University Press
Page : 656 pages
File Size : 50,7 Mb
Release : 2003-04-28
Category : Mathematics
ISBN : 9781139439138

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Complex Variables by Mark J. Ablowitz,Athanassios S. Fokas Pdf

Complex variables provide powerful methods for attacking problems that can be very difficult to solve in any other way, and it is the aim of this book to provide a thorough grounding in these methods and their application. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, and numerical methods. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann–Hilbert problems. The authors provide an extensive array of applications, illustrative examples and homework exercises. This 2003 edition was improved throughout and is ideal for use in undergraduate and introductory graduate level courses in complex variables.

Author : James Ward Brown,Ruel Vance Churchill
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 168 pages
File Size : 44,8 Mb
Release : 2003-03
Category : Mathematics
ISBN : 0072878347

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Student Solutions Manual to Accompany Complex Variables and Applications by James Ward Brown,Ruel Vance Churchill Pdf

Author : H. S. KASANA
Publisher : PHI Learning Pvt. Ltd.
Page : 510 pages
File Size : 54,6 Mb
Release : 2005-01-01
Category : Mathematics
ISBN : 8120326415

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COMPLEX VARIABLES by H. S. KASANA Pdf

The second edition of this comprehensive and accessible text continues to offer students a challenging and enjoyable study of complex variables that is infused with perfect balanced coverage of mathematical theory and applied topics. The author explains fundamental concepts and techniques with precision and introduces the students to complex variable theory through conceptual develop-ment of analysis that enables them to develop a thorough understanding of the topics discussed. Geometric interpretation of the results, wherever necessary, has been inducted for making the analysis more accessible. The level of the text assumes that the reader is acquainted with elementary real analysis. Beginning with the revision of the algebra of complex variables, the book moves on to deal with analytic functions, elementary functions, complex integration, sequences, series and infinite products, series expansions, singularities and residues. The application-oriented chapters on sums and integrals, conformal mappings, Laplace transform, and some special topics, provide a practical-use perspective. Enriched with many numerical examples and exercises designed to test the student's comprehension of the topics covered, this book is written for a one-semester course in complex variables for students in the science and engineering disciplines.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 243 pages
File Size : 41,7 Mb
Release : 2019-04-16
Category : Mathematics
ISBN : 9781000007183

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Complex Variables by Steven G. Krantz Pdf

The idea of complex numbers dates back at least 300 years—to Gauss and Euler, among others. Today complex analysis is a central part of modern analytical thinking. It is used in engineering, physics, mathematics, astrophysics, and many other fields. It provides powerful tools for doing mathematical analysis, and often yields pleasing and unanticipated answers. This book makes the subject of complex analysis accessible to a broad audience. The complex numbers are a somewhat mysterious number system that seems to come out of the blue. It is important for students to see that this is really a very concrete set of objects that has very concrete and meaningful applications. Features: This new edition is a substantial rewrite, focusing on the accessibility, applied, and visual aspect of complex analysis This book has an exceptionally large number of examples and a large number of figures. The topic is presented as a natural outgrowth of the calculus. It is not a new language, or a new way of thinking. Incisive applications appear throughout the book. Partial differential equations are used as a unifying theme.

Author : James Ward Brown,Ruel Vance Churchill
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 426 pages
File Size : 42,6 Mb
Release : 1996
Category : Computers
ISBN : UVA:X002701498

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Complex Variables and Applications by James Ward Brown,Ruel Vance Churchill Pdf

This text, and accompanying disk, provides coverage of complex variables. It uses examples and exercise sets, with clear explanations of problem-solving techniqes and material on the further theory of functions.

Author : Steven G. Krantz
Publisher : CRC Press
Page : 440 pages
File Size : 53,6 Mb
Release : 2007-09-19
Category : Mathematics
ISBN : 9781420010954

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Complex Variables by Steven G. Krantz Pdf

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.

Author : Mark J. Ablowitz,A. S. Fokas
Publisher : Cambridge University Press
Page : 656 pages
File Size : 47,6 Mb
Release : 2003-04-28
Category : Mathematics
ISBN : 0521534291

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Complex Variables by Mark J. Ablowitz,A. S. Fokas Pdf

This 2003 edition is ideal for use in undergraduate and introductory graduate level courses in complex variables.

Author : John Wermer
Publisher : Springer Science & Business Media
Page : 169 pages
File Size : 46,7 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475738780

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Banach Algebras and Several Complex Variables by John Wermer Pdf

During the past twenty years many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. On the one hand, function theory has been used to answer algebraic questions such as the question of the existence of idempotents in a Banach algebra. On the other hand, concepts arising from the study of Banach algebras such as the maximal ideal space, the Silov boundary, Gleason parts, etc. have led to new questions and to new methods of proof in function theory. Roughly one third of this book isconcerned with developing some of the principal applications of function theory in several complex variables to Banach algebras. We presuppose no knowledge of severalcomplex variables on the part of the reader but develop the necessary material from scratch. The remainder of the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. For n > I no complete theory exists but many important particular problems have been solved. Throughout, our aim has been to make the exposition elementary and self-contained. We have cheerfully sacrificed generality and completeness all along the way in order to make it easier to understand the main ideas.

Author : Mark J. Ablowitz,Athanassios S. Fokas
Publisher : Cambridge University Press
Page : 421 pages
File Size : 50,7 Mb
Release : 2021-03-25
Category : Mathematics
ISBN : 9781108832618

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Introduction to Complex Variables and Applications by Mark J. Ablowitz,Athanassios S. Fokas Pdf

An introduction to complex variables that caters for undergraduate students in applied mathematics, science, and engineering.

Author : A. David Wunsch
Publisher : Pearson
Page : 0 pages
File Size : 44,6 Mb
Release : 2005
Category : Functions of complex variables
ISBN : 0201756099

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Complex Variables with Applications by A. David Wunsch Pdf

The third edition of this unique text remains accessible to students of engineering, physics and applied mathematics with varying mathematical backgrounds. Designed for a one or two-semester course in complex analysis, there is optional review material on elementary calculus. Complex Numbers; The Complex Function and its Derivative; The Basic Transcendental Functions; Integration in the Complex Plane; Infinite Series Involving a Complex Variable; Residues and Their Use in Integration; Laplace Transforms and Stability of Systems; Conformal Mapping and Some of Its Applications; Advanced Topics in Infinite Series and Products For all readers interested in complex variables with applications.

Author : Nakhlé H. Asmar,Loukas Grafakos
Publisher : Springer
Page : 494 pages
File Size : 54,5 Mb
Release : 2018-10-12
Category : Mathematics
ISBN : 9783319940632

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Complex Analysis with Applications by Nakhlé H. Asmar,Loukas Grafakos Pdf

This textbook is intended for a one semester course in complex analysis for upper level undergraduates in mathematics. Applications, primary motivations for this text, are presented hand-in-hand with theory enabling this text to serve well in courses for students in engineering or applied sciences. The overall aim in designing this text is to accommodate students of different mathematical backgrounds and to achieve a balance between presentations of rigorous mathematical proofs and applications. The text is adapted to enable maximum flexibility to instructors and to students who may also choose to progress through the material outside of coursework. Detailed examples may be covered in one course, giving the instructor the option to choose those that are best suited for discussion. Examples showcase a variety of problems with completely worked out solutions, assisting students in working through the exercises. The numerous exercises vary in difficulty from simple applications of formulas to more advanced project-type problems. Detailed hints accompany the more challenging problems. Multi-part exercises may be assigned to individual students, to groups as projects, or serve as further illustrations for the instructor. Widely used graphics clarify both concrete and abstract concepts, helping students visualize the proofs of many results. Freely accessible solutions to every-other-odd exercise are posted to the book’s Springer website. Additional solutions for instructors’ use may be obtained by contacting the authors directly.

Author : Joseph L. Taylor
Publisher : American Mathematical Soc.
Page : 319 pages
File Size : 51,7 Mb
Release : 2011
Category : Functions of complex variables
ISBN : 9780821869017

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Complex Variables by Joseph L. Taylor Pdf

"The text covers a broad spectrum between basic and advanced complex variables on the one hand and between theoretical and applied or computational material on the other hand. With careful selection of the emphasis put on the various sections, examples, and exercises, the book can be used in a one- or two-semester course for undergraduate mathematics majors, a one-semester course for engineering or physics majors, or a one-semester course for first-year mathematics graduate students. It has been tested in all three settings at the University of Utah. The exposition is clear, concise, and lively. There is a clean and modern approach to Cauchy's theorems and Taylor series expansions, with rigorous proofs but no long and tedious arguments. This is followed by the rich harvest of easy consequences of the existence of power series expansions. Through the central portion of the text, there is a careful and extensive treatment of residue theory and its application to computation of integrals, conformal mapping and its applications to applied problems, analytic continuation, and the proofs of the Picard theorems. Chapter 8 covers material on infinite products and zeroes of entire functions. This leads to the final chapter which is devoted to the Riemann zeta function, the Riemann Hypothesis, and a proof of the Prime Number Theorem." -- Publisher.