Complex Analytic Functions Theory And Applications
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Complex Analytic Functions Theory And Applications
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Author : S. K. Sharma
language : en
Publisher: New Age International
Release Date : 2000
Complex Analytic Functions Theory And Applications written by S. K. Sharma and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with categories.
In A Simple And Interesting Style, This Book Explains The Various Concepts In Complex Analysis And Illustrates Them Through Practical Applications. Starting With A Definition Of The Properties Of A Complex Number, The Book Goes On To Explain Complex Variables And Conformal Mapping. It Then Presents An Exhaustive Description Of Schwarz -Christoffel Transformation Which Is Followed By A Discussion Of Complex Integration And Singularities And Residues.The Book Explains Both Simple And Sophisticated Applications. In The Former Category Are Mechanical Vibrating Systems, Electric Circuits Etc., While In The Latter Category Are Problems In The Theory Of Heat, Fluid Mechanics, Electrostatics, Dam Designs Etc.With Its Rich And Lively Discussion Of An Important Mathematical Method, This Book Would Be Extremely Useful For Both Science And Engineering Students. Researchers And Practising Engineers Would Also Find It A Valuable Reference Source.
Fundamentals Of Complex Analysis
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Author : K. K. Dube
language : en
Publisher: I. K. International Pvt Ltd
Release Date : 2013-12-30
Fundamentals Of Complex Analysis written by K. K. Dube and has been published by I. K. International Pvt Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-30 with Calculus categories.
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
Generalized Analytic Functions
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Author : Helmut Florian
language : en
Publisher: Springer
Release Date : 1998-05-31
Generalized Analytic Functions written by Helmut Florian and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-05-31 with Mathematics categories.
Contains papers from a January 1997 conference at the Technical University of Graz. Part I looks at generalized analytic functions, dealing not only with problems in the complex plane but also related problems in higher dimensions where several complex variables and Clifford Analysis are used. Part II is devoted to applications of partial differential equations to mechanics, with contributions on boundary elements and asymptotic methods, and hemivariational inequalities. A substantial number of papers in Part II deal with problems of ocean acoustics. No index. Annotation copyrighted by Book News, Inc., Portland, OR
Complex Variables
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Author : H. S. KASANA
language : en
Publisher: PHI Learning Pvt. Ltd.
Release Date : 2005-01-01
Complex Variables written by H. S. KASANA and has been published by PHI Learning Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-01-01 with Mathematics categories.
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.
Introductory Complex And Analysis Applications
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Author : William R. Derrick
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Introductory Complex And Analysis Applications written by William R. Derrick and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics, including integral transforms, asymptotic expansions, harmonic functions, Fourier transformation, and infinite series. Organized into eight chapters, this book begins with an overview of the theory of functions of a complex variable. This text then examines the properties of analytical functions, which are all consequences of the differentiability of the function. Other chapters consider the converse of Taylor's Theorem, namely that convergent power series are analytical functions in their domain of convergence. This book discusses as well the Residue Theorem, which is of fundamental significance in complex analysis and is the core concept in the development of the techniques. The final chapter deals with the method of steepest descent, which is useful in determining the asymptotic behavior of integral representations of analytic functions. This book is a valuable resource for undergraduate students in engineering and mathematics.
Complex Analysis And Its Applications To Control Theory
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Author : Andrei E. Vityaev
language : en
Publisher:
Release Date : 1996
Complex Analysis And Its Applications To Control Theory written by Andrei E. Vityaev and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Complex Analysis
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Author : John Stalker
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-03
Complex Analysis written by John Stalker and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-10-03 with Mathematics categories.
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.
Complex Analysis With Applications
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Author : Nakhlé H. Asmar
language : en
Publisher: Springer
Release Date : 2018-10-12
Complex Analysis With Applications written by Nakhlé H. Asmar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-12 with Mathematics categories.
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.
Analytic Function Theory Of Several Variables
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Author : Junjiro Noguchi
language : en
Publisher: Springer
Release Date : 2016-08-16
Analytic Function Theory Of Several Variables written by Junjiro Noguchi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-16 with Mathematics categories.
The purpose of this book is to present the classical analytic function theory of several variables as a standard subject in a course of mathematics after learning the elementary materials (sets, general topology, algebra, one complex variable). This includes the essential parts of Grauert–Remmert's two volumes, GL227(236) (Theory of Stein spaces) and GL265 (Coherent analytic sheaves) with a lowering of the level for novice graduate students (here, Grauert's direct image theorem is limited to the case of finite maps).The core of the theory is "Oka's Coherence", found and proved by Kiyoshi Oka. It is indispensable, not only in the study of complex analysis and complex geometry, but also in a large area of modern mathematics. In this book, just after an introductory chapter on holomorphic functions (Chap. 1), we prove Oka's First Coherence Theorem for holomorphic functions in Chap. 2. This defines a unique character of the book compared with other books on this subject, in which the notion of coherence appears much later.The present book, consisting of nine chapters, gives complete treatments of the following items: Coherence of sheaves of holomorphic functions (Chap. 2); Oka–Cartan's Fundamental Theorem (Chap. 4); Coherence of ideal sheaves of complex analytic subsets (Chap. 6); Coherence of the normalization sheaves of complex spaces (Chap. 6); Grauert's Finiteness Theorem (Chaps. 7, 8); Oka's Theorem for Riemann domains (Chap. 8). The theories of sheaf cohomology and domains of holomorphy are also presented (Chaps. 3, 5). Chapter 6 deals with the theory of complex analytic subsets. Chapter 8 is devoted to the applications of formerly obtained results, proving Cartan–Serre's Theorem and Kodaira's Embedding Theorem. In Chap. 9, we discuss the historical development of "Coherence".It is difficult to find a book at this level that treats all of the above subjects in a completely self-contained manner. In the present volume, a number of classical proofs are improved and simplified, so that the contents are easily accessible for beginning graduate students.
Advances In Complex Analysis And Applications
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Author : Francisco Bulnes
language : en
Publisher: BoD – Books on Demand
Release Date : 2020-11-04
Advances In Complex Analysis And Applications written by Francisco Bulnes and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-04 with Computers categories.
The complex analysis, also known as theory of analytic functions or complex variable function theory, is the part of mathematical analysis that investigates the functions of complex numbers, their analyticity, holomorphicity, and integration of these functions on complex domains that can be complex manifolds or submanifolds. Also the extensions of these domains to the complex projective spaces and complex topological groups are study themes. The analytic continuing of complex domains where complex series representations are used and the exploring of singularities whose integration invariants obtain values as zeros of certain polynomials of the complex rings of certain vector bundles are important in the exploring of new function classes in the meromorphic context and also arithmetic context. Also important are established correspondences with complex vector spaces, or even in their real parts, using several techniques of complex geometrical analysis, Nevanlinna methods, and other techniques as the modular forms. All this is just some examples of great abundance of the problems in mathematics research that require the complex analysis application. This book covers some interesting and original research of certain topics of complex analysis. Also included are some applications for inverse and ill posed problems developed in engineering and applied research.