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Fundamentals Of Complex Analysis Theory And Applications

Author: K K Dube
Publisher: I. K. International Pvt Ltd
ISBN: 9380026021
Size: 41.31 MB
Format: PDF, ePub, Docs
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The book divided in ten chapters deals with: " Algebra of complex numbers and its various geometrical properties, properties of polar form of complex numbers and regions in the complex plane. " Limit, continuity, differentiability. " Different kinds of complex valued functions. " Different types of transformations. " Conformal mappings of different functions. " Properties of bilinear and special bilinear transformation. " Line integrals, their properties and different theorems. " Sequences and series, Power series, Zero s of functions, residues and residue theorem, meromorphic functions, different kinds of singularities. " Evaluation of real integrals. " Analytic continuation, construction of harmonic functions, infinite product, their properties and Gamma function. " Schwarz-Christoffel transformations, mapping by multi valued functions, entire functions. " Jenson s theorem and Poisson-Jenson theorem. The book is designed as a textbook for UG and PG students of science as well as engineering

Complex Analysis With Applications

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 9780486647623
Size: 31.45 MB
Format: PDF, ePub
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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.

Complex Analysis

Author: John Stalker
Publisher: Springer Science & Business Media
ISBN: 0817649190
Size: 55.35 MB
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All modem introductions to complex analysis follow, more or less explicitly, the pattern laid down in Whittaker and Watson [75]. In "part I'' we find the foundational material, the basic definitions and theorems. In "part II" we find the examples and applications. Slowly we begin to understand why we read part I. Historically this is an anachronism. Pedagogically it is a disaster. Part II in fact predates part I, so clearly it can be taught first. Why should the student have to wade through hundreds of pages before finding out what the subject is good for? In teaching complex analysis this way, we risk more than just boredom. Beginning with a series of unmotivated definitions gives a misleading impression of complex analy sis in particular and of mathematics in general. The classical theory of analytic functions did not arise from the idle speculation of bored mathematicians on the possible conse quences of an arbitrary set of definitions; it was the natural, even inevitable, consequence of the practical need to answer questions about specific examples. In standard texts, after hundreds of pages of theorems about generic analytic functions with only the rational and trigonometric functions as examples, students inevitably begin to believe that the purpose of complex analysis is to produce more such theorems. We require introductory com plex analysis courses of our undergraduates and graduates because it is useful both within mathematics and beyond.

Functions Of A Complex Variable And Some Of Their Applications

Author: B. A. Fuchs
Publisher: Elsevier
ISBN: 1483155056
Size: 50.87 MB
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Functions of a Complex Variable and Some of Their Applications, Volume 1, discusses the fundamental ideas of the theory of functions of a complex variable. The book is the result of a complete rewriting and revision of a translation of the second (1957) Russian edition. Numerous changes and additions have been made, both in the text and in the solutions of the Exercises. The book begins with a review of arithmetical operations with complex numbers. Separate chapters discuss the fundamentals of complex analysis; the concept of conformal transformations; the most important of the elementary functions; and the complex potential for a plane vector field and the application of the simplest methods of function theory to the analysis of such a field. Subsequent chapters cover the fundamental apparatus of the theory of regular functions, i.e. basic integral theorems and expansions in series; the general concept of an analytic function; applications of the theory of residues; and polygonal domain mapping. This book is intended for undergraduate and postgraduate students of higher technical institutes and for engineers wishing to increase their knowledge of theory.

Complex Variables

Author: H. S. KASANA
Publisher: PHI Learning Pvt. Ltd.
ISBN: 9788120326415
Size: 29.52 MB
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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.

Complex Analysis With Applications In Science And Engineering

Author: Harold Cohen
Publisher: Springer Science & Business Media
ISBN: 0387730583
Size: 75.92 MB
Format: PDF, ePub
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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.

Introductory Complex Analysis

Author: Richard A. Silverman
Publisher: Courier Corporation
ISBN: 0486318524
Size: 58.52 MB
Format: PDF
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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.

Foundations Of Complex Analysis

Author: Saminathan Ponnusamy
Publisher: Alpha Science International, Limited
ISBN: 9781842652237
Size: 45.71 MB
Format: PDF, ePub, Mobi
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Suitable for a two semester course in complex analysis, or as a supplementary text for an advanced course in function theory, this book aims to give students a good foundation of complex analysis and provides a basis for solving problems in mathematics, physics, engineering and many other sciences.