Author: Saminathan Ponnusamy,Herb Silverman

Publisher: Springer Science & Business Media

ISBN: 9780817645137

Category: Mathematics

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## Complex Variables with Applications

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
## Complex Variables

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.
## Complex Variables and Applications

## Complex Variables With Applications, 3/E

## Complex variables with physical applications

## Complex Variables and Their Applications

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.
## COMPLEX VARIABLES

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.
## Several Complex Variables with Connections to Algebraic Geometry and Lie Groups

This text presents an integrated development of the theory of several complex variables and complex algebraic geometry, leading to proofs of Serre's celebrated GAGA theorems relating the two subjects, and including applications to the representation theory of complex semisimple Lie groups. It includes a thorough treatment of the local theory using the tools of commutative algebra, an extensive development of sheaf theory and the theory of coherent analytic and algebraic sheaves, proofs of the main vanishing theorems for these categories of sheaves, and a complete proof of the finite dimensionality of the cohomology of coherent sheaves on compact varieties. The vanishing theorems have a wide variety of applications and these are covered in detail. Of particular interest are the last three chapters, which are devoted to applications of the preceding material to the study of the structure and representations of complex semisimple Lie groups.Included in this text are introductions to harmonic analysis, the Peter-Weyl theorem, Lie theory and the structure of Lie algebras, semisimple Lie algebras and their representations, algebraic groups and the structure of complex semisimple Lie groups. All of this culminates in Milicic's proof of the Borel-Weil-Bott theorem, which makes extensive use of the material developed earlier in the text. There are numerous examples and exercises in each chapter. This modern treatment of a classic point of view would be an excellent text for a graduate course on several complex variables, as well as a useful reference for the expert.
## Complex Analysis with Applications

The basics of what every scientist and engineer should know, from complex numbers, limits in the complex plane, and complex functions to Cauchy's theory, power series, and applications of residues. 1974 edition.
## Functions of a Complex Variable

## Applied Complex Variables

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

This textbook introduces the theory of complex variables at undergraduate level. A good collection of problems is provided in the second part of the book. The book is written in a user-friendly style that presents important fundamentals a beginner needs to master the technical details of the subject. Similarly, teachers can also adopt the text for a course on complex variables and for mining problems. The organization of problems into focused sets is an important feature of the book.
## A MatLab® Companion to Complex Variables

This book is intended for someone learning functions of a complex variable and who enjoys using MATLAB. It will enhance the exprience of learning complex variable theory and will strengthen the knowledge of someone already trained in ths branch of advanced calculus. ABET, the accrediting board for engineering programs, makes it clear that engineering graduates must be skilled in the art of programming in a language such as MATLAB®. Supplying students with a bridge between the functions of complex variable theory and MATLAB, this supplemental text enables instructors to easily add a MATLAB component to their complex variables courses. A MATLAB® Companion to Complex Variables provides readers with a clear understanding of the utility of MATLAB in complex variable calculus. An ideal adjunct to standard texts on the functions of complex variables, the book allows professors to quickly find and assign MATLAB programming problems that will strengthen students’ knowledge of the language and concepts of complex variable theory. The book shows students how MATLAB can be a powerful learning aid in such staples of complex variable theory as conformal mapping, infinite series, contour integration, and Laplace and Fourier transforms. In addition to MATLAB programming problems, the text includes many examples in each chapter along with MATLAB code. Fractals, the most recent interesting topic involving complex variables, demands to be treated with a language such as MATLAB. This book concludes with a Coda, which is devoted entirely to this visually intriguing subject. MATLAB is not without constraints, limitations, irritations, and quirks, and there are subtleties involved in performing the calculus of complex variable theory with this language. Without knowledge of these subtleties, engineers or scientists attempting to use MATLAB for solutions of practical problems in complex variable theory suffer the risk of making major mistakes. This book serves as an early warning system about these pitfalls.
## Fundamentals of Complex Analysis

Originally published in 2003, reissued as part of Pearson's modern classic series.
## Complex Analysis with Applications in Science and Engineering

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.
## Handbook of Complex Variables

This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.
## Complex Variables

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: harmonic and analytic functions

## A Guide to Complex Variables

A quick and easy-to-use introduction to the key topics in complex variables, for mathematicians and non-mathematicians alike.

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Author: Saminathan Ponnusamy,Herb Silverman

Publisher: Springer Science & Business Media

ISBN: 9780817645137

Category: Mathematics

Page: 514

View: 4835

*A Physical Approach with Applications and MATLAB*

Author: Steven G. Krantz

Publisher: CRC Press

ISBN: 1584885807

Category: Mathematics

Page: 440

View: 1182

Author: Brown

Publisher: McGraw-Hill Higher Education

ISBN: 0073530859

Category:

Page: N.A

View: 996

Author: Wunsch

Publisher: Pearson Education India

ISBN: 9788131728574

Category:

Page: 696

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Author: Arthur A. Hauser

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 418

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Author: Anthony D. Osborne

Publisher: Addison-Wesley

ISBN: N.A

Category: Mathematics

Page: 454

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*THEORY AND APPLICATIONS*

Author: H. S. KASANA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 9788120326415

Category: Mathematics

Page: 504

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Author: Joseph L. Taylor

Publisher: American Mathematical Soc.

ISBN: 082183178X

Category: Mathematics

Page: 507

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Author: Richard A. Silverman

Publisher: Courier Corporation

ISBN: 9780486647623

Category: Mathematics

Page: 274

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*With Applications*

Author: Edgar Giraldus Phillips

Publisher: N.A

ISBN: N.A

Category: Calculus

Page: 144

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Author: John W. Dettman

Publisher: Courier Corporation

ISBN: 0486158284

Category: Mathematics

Page: 512

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*Principles and Problem Sessions*

Author: A. K. Kapoor

Publisher: World Scientific

ISBN: 9814313521

Category: Mathematics

Page: 495

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Author: A. David Wunsch

Publisher: CRC Press

ISBN: 1498755682

Category: Mathematics

Page: 344

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*With Applications to Engineering and Science (Classic Version)*

Author: Edward Saff,Arthur D. Snider

Publisher: Math Classics

ISBN: 9780134689487

Category: Mathematics

Page: 576

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Author: Harold Cohen

Publisher: Springer Science & Business Media

ISBN: 0387730583

Category: Mathematics

Page: 477

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Author: Steven G Krantz

Publisher: Springer Science & Business Media

ISBN: 1461215889

Category: Mathematics

Page: 290

View: 2619

Author: Robert B. Ash

Publisher: Academic Press

ISBN: 1483216195

Category: Mathematics

Page: 264

View: 1861

Author: Francis J. Flanigan

Publisher: N.A

ISBN: N.A

Category: Analytic functions

Page: 353

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Author: Steven G. Krantz

Publisher: MAA

ISBN: 9780883853382

Category: Mathematics

Page: 182

View: 7364