Complex Functions An Introduction To Complex Analysis
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Visual Complex Functions
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Author : Elias Wegert
language : en
Publisher: Birkhäuser
Release Date : 2012-08-29
Visual Complex Functions written by Elias Wegert and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-29 with Mathematics categories.
This book provides a systematic introduction to functions of one complex variable. Its novel feature is the consistent use of special color representations – so-called phase portraits – which visualize functions as images on their domains. Reading Visual Complex Functions requires no prerequisites except some basic knowledge of real calculus and plane geometry. The text is self-contained and covers all the main topics usually treated in a first course on complex analysis. With separate chapters on various construction principles, conformal mappings and Riemann surfaces it goes somewhat beyond a standard programme and leads the reader to more advanced themes. In a second storyline, running parallel to the course outlined above, one learns how properties of complex functions are reflected in and can be read off from phase portraits. The book contains more than 200 of these pictorial representations which endow individual faces to analytic functions. Phase portraits enhance the intuitive understanding of concepts in complex analysis and are expected to be useful tools for anybody working with special functions – even experienced researchers may be inspired by the pictures to new and challenging questions. Visual Complex Functions may also serve as a companion to other texts or as a reference work for advanced readers who wish to know more about phase portraits.
An Introduction To Complex Analysis
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Author : Ravi P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-01
An Introduction To Complex Analysis written by Ravi P. Agarwal 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 2011-07-01 with Mathematics categories.
This textbook introduces the subject of complex analysis to advanced undergraduate and graduate students in a clear and concise manner. Key features of this textbook: effectively organizes the subject into easily manageable sections in the form of 50 class-tested lectures, uses detailed examples to drive the presentation, includes numerous exercise sets that encourage pursuing extensions of the material, each with an “Answers or Hints” section, covers an array of advanced topics which allow for flexibility in developing the subject beyond the basics, provides a concise history of complex numbers. An Introduction to Complex Analysis will be valuable to students in mathematics, engineering and other applied sciences. Prerequisites include a course in calculus.
An Introduction To Complex Function Theory
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Author : Bruce P. Palka
language : en
Publisher: Springer Science & Business Media
Release Date : 1991
An Introduction To Complex Function Theory written by Bruce P. Palka 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 1991 with Mathematics categories.
This book provides a rigorous yet elementary introduction to the theory of analytic functions of a single complex variable. While presupposing in its readership a degree of mathematical maturity, it insists on no formal prerequisites beyond a sound knowledge of calculus. Starting from basic definitions, the text slowly and carefully develops the ideas of complex analysis to the point where such landmarks of the subject as Cauchy's theorem, the Riemann mapping theorem, and the theorem of Mittag-Leffler can be treated without sidestepping any issues of rigor. The emphasis throughout is a geometric one, most pronounced in the extensive chapter dealing with conformal mapping, which amounts essentially to a "short course" in that important area of complex function theory. Each chapter concludes with a wide selection of exercises, ranging from straightforward computations to problems of a more conceptual and thought-provoking nature.
Complex Analysis
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Author : Lars Ahlfors
language : en
Publisher:
Release Date : 1979
Complex Analysis written by Lars Ahlfors and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Education categories.
A standard source of information of functions of one complex variable, this text has retained its wide popularity in this field by being consistently rigorous without becoming needlessly concerned with advanced or overspecialized material. Difficult points have been clarified, the book has been reviewed for accuracy, and notations and terminology have been modernized. Chapter 2, Complex Functions, features a brief section on the change of length and area under conformal mapping, and much of Chapter 8, Global-Analytic Functions, has been rewritten in order to introduce readers to the terminology of germs and sheaves while still emphasizing that classical concepts are the backbone of the theory. Chapter 4, Complex Integration, now includes a new and simpler proof of the general form of Cauchy's theorem. There is a short section on the Riemann zeta function, showing the use of residues in a more exciting situation than in the computation of definite integrals.
Introduction To Analysis With Complex Numbers
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Author : Irena Swanson
language : en
Publisher: World Scientific Publishing Company
Release Date : 2021
Introduction To Analysis With Complex Numbers written by Irena Swanson and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Mathematical analysis categories.
This is a self-contained book that covers the standard topics in introductory analysis and that in addition, constructs the natural, rational, real and complex numbers, also handles complex-valued functions, sequences, and series. The book teaches how to write proofs. Fundamental proof-writing logic is covered in Chapter 1 and is repeated and enhanced in two appendices. Many examples of proofs appear with words in a different font for what should be going on in the proof writer's head. The book contains many examples and exercises to solidify the understanding. The material is presented rigorously with proofs and with many worked-out examples. Exercises are varied, many involve proofs, and some provide additional learning materials.
Introduction To Complex Analysis In Several Variables
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Author : Volker Scheidemann
language : en
Publisher: Springer Nature
Release Date : 2023-04-26
Introduction To Complex Analysis In Several Variables written by Volker Scheidemann and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-26 with Mathematics categories.
This book gives a comprehensive introduction to complex analysis in several variables. While it focusses on a number of topics in complex analysis rather than trying to cover as much material as possible, references to other parts of mathematics such as functional analysis or algebras are made to help broaden the view and the understanding of the chosen topics. A major focus are extension phenomena alien to the one-dimensional theory, which are expressed in the famous Hartog's Kugelsatz, the theorem of Cartan-Thullen, and Bochner's theorem. The book aims primarily at students starting to work in the field of complex analysis in several variables and instructors preparing a course. To that end, a lot of examples and supporting exercises are provided throughout the text. This second edition includes hints and suggestions for the solution of the provided exercises, with various degrees of support.
Complex Analysis
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Author : Eberhard Freitag
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Complex Analysis written by Eberhard Freitag 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 2006-01-17 with Mathematics categories.
All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed Provides a more in-depth introduction to the subject than other existing books in this area Over 400 exercises including hints for solutions are included
Complex Analysis 2
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Author : Eberhard Freitag
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-10
Complex Analysis 2 written by Eberhard Freitag 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 2011-06-10 with Mathematics categories.
The book contains a complete self-contained introduction to highlights of classical complex analysis. New proofs and some new results are included. All needed notions are developed within the book: with the exception of some basic facts which can be found in the ̄rst volume. There is no comparable treatment in the literature.
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables
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Author : Henri Cartan
language : en
Publisher: Courier Corporation
Release Date : 2013-04-22
Elementary Theory Of Analytic Functions Of One Or Several Complex Variables written by Henri Cartan and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
Basic treatment includes existence theorem for solutions of differential systems where data is analytic, holomorphic functions, Cauchy's integral, Taylor and Laurent expansions, more. Exercises. 1973 edition.
A Course In Complex Analysis
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Author : Wolfgang Fischer
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-21
A Course In Complex Analysis written by Wolfgang Fischer 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 2011-10-21 with Mathematics categories.
This carefully written textbook is an introduction to the beautiful concepts and results of complex analysis. It is intended for international bachelor and master programmes in Germany and throughout Europe; in the Anglo-American system of university education the content corresponds to a beginning graduate course. The book presents the fundamental results and methods of complex analysis and applies them to a study of elementary and non-elementary functions (elliptic functions, Gamma- and Zeta function including a proof of the prime number theorem ...) and – a new feature in this context! – to exhibiting basic facts in the theory of several complex variables. Part of the book is a translation of the authors’ German text “Einführung in die komplexe Analysis”; some material was added from the by now almost “classical” text “Funktionentheorie” written by the authors, and a few paragraphs were newly written for special use in a master’s programme.