Visual Complex Analysis

Visual Complex Analysis Author Tristan Needham
ISBN-10 0198534469
Year 1998
Pages 592
Language en
Publisher Oxford University Press
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Now available in paperback, this successful radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. With several hundred diagrams, and far fewer prerequisites than usual, this is the first visual intuitive introduction to complex analysis. Although designed for use by undergraduates in mathematics and science, the novelty of the approach will also interest professional mathematicians.

Visual Complex Functions

Visual Complex Functions Author Elias Wegert
ISBN-10 9783034801805
Year 2012-08-30
Pages 360
Language en
Publisher Springer Science & Business Media
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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.

Complex Analysis

Complex Analysis Author Joseph Bak
ISBN-10 1441972889
Year 2010-08-02
Pages 328
Language en
Publisher Springer Science & Business Media
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This unusual and lively textbook offers a clear and intuitive approach to the classical and beautiful theory of complex variables. With very little dependence on advanced concepts from several-variable calculus and topology, the text focuses on the authentic complex-variable ideas and techniques. Accessible to students at their early stages of mathematical study, this full first year course in complex analysis offers new and interesting motivations for classical results and introduces related topics stressing motivation and technique. Numerous illustrations, examples, and now 300 exercises, enrich the text. Students who master this textbook will emerge with an excellent grounding in complex analysis, and a solid understanding of its wide applicability.

Theory of Complex Functions

Theory of Complex Functions Author Reinhold Remmert
ISBN-10 9781461209393
Year 2012-12-06
Pages 458
Language en
Publisher Springer Science & Business Media
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A lively and vivid look at the material from function theory, including the residue calculus, supported by examples and practice exercises throughout. There is also ample discussion of the historical evolution of the theory, biographical sketches of important contributors, and citations - in the original language with their English translation - from their classical works. Yet the book is far from being a mere history of function theory, and even experts will find a few new or long forgotten gems here. Destined to accompany students making their way into this classical area of mathematics, the book offers quick access to the essential results for exam preparation. Teachers and interested mathematicians in finance, industry and science will profit from reading this again and again, and will refer back to it with pleasure.

Complex Variables

Complex Variables Author Francis J. Flanigan
ISBN-10 9780486318486
Year 2013-08-16
Pages 384
Language en
Publisher Courier Corporation
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Contents include calculus in the plane; harmonic functions in the plane; analytic functions and power series; singular points and Laurent series; and much more. Numerous problems and solutions. 1972 edition.

Functions of One Complex Variable

Functions of One Complex Variable Author J.B. Conway
ISBN-10 9781461599722
Year 2012-12-06
Pages 313
Language en
Publisher Springer Science & Business Media
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This book is intended as a textbook for a first course in the theory of functions of one complex variable for students who are mathematically mature enough to understand and execute E - I) arguments. The actual pre requisites for reading this book are quite minimal; not much more than a stiff course in basic calculus and a few facts about partial derivatives. The topics from advanced calculus that are used (e.g., Leibniz's rule for differ entiating under the integral sign) are proved in detail. Complex Variables is a subject which has something for all mathematicians. In addition to having applications to other parts of analysis, it can rightly claim to be an ancestor of many areas of mathematics (e.g., homotopy theory, manifolds). This view of Complex Analysis as "An Introduction to Mathe matics" has influenced the writing and selection of subject matter for this book. The other guiding principle followed is that all definitions, theorems, etc.

Problems and Solutions for Complex Analysis

Problems and Solutions for Complex Analysis Author Rami Shakarchi
ISBN-10 9781461215349
Year 2012-12-06
Pages 246
Language en
Publisher Springer Science & Business Media
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All the exercises plus their solutions for Serge Lang's fourth edition of "Complex Analysis," ISBN 0-387-98592-1. The problems in the first 8 chapters are suitable for an introductory course at undergraduate level and cover power series, Cauchy's theorem, Laurent series, singularities and meromorphic functions, the calculus of residues, conformal mappings, and harmonic functions. The material in the remaining 8 chapters is more advanced, with problems on Schwartz reflection, analytic continuation, Jensen's formula, the Phragmen-Lindeloef theorem, entire functions, Weierstrass products and meromorphic functions, the Gamma function and Zeta function. Also beneficial for anyone interested in learning complex analysis.

Introduction to Circle Packing

Introduction to Circle Packing Author Kenneth Stephenson
ISBN-10 0521823560
Year 2005
Pages 356
Language en
Publisher Cambridge University Press
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Kenneth Stephenson introduces a new mathematical topic known as 'circle packing', taking the reader from first definitions to latest theory, computations and applications.

Introduction to Complex Analysis

Introduction to Complex Analysis Author Hilary A Priestley
ISBN-10 9780198525622
Year 2003
Pages 328
Language en
Publisher Oxford University Press, USA
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Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise sets have been substantially revised and enlarged, with carefully graded exercises at the end of each chapter. This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks for Pattern Recognition, Gelman and Nolan: Teaching Statistics.

Invitation to Complex Analysis

Invitation to Complex Analysis Author Ralph P. Boas
ISBN-10 9780883857649
Year 2010-08-12
Pages 327
Language en
Publisher MAA
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An ideal choice for a first course in complex analysis, this book can be used either as a classroom text or for independent study. Written in an informal style by a master expositor, the book distills more than half a century of experience with the subject into a lucid, engaging, yet rigorous account. The book reveals both the power of complex analysis as a tool for applications and the intrinsic beauty of the subject as a fundamental part of pure mathematics. Written at the level of courses commonly taught in American universities to seniors and beginning graduate students, the book is suitable for readers acquainted with advanced calculus or introductory real analysis. The treatment goes beyond the standard material of power series, Cauchy's theorem, residues, conformal mapping, and harmonic functions by including accessible discussions of many intriguing topics that are uncommon in a book at this level. Readers will encounter notions ranging from Landau's notation to overconvergent series to the Phragmén-Lindelöf theorem. The flexibility afforded by the supplementary topics and applications makes the book adaptable either to a short, one-term course or to a comprehensive, full-year course.The writing is user-friendly in many ways. Each topic is discussed in a typical, commonly encountered situation rather than in the most general, abstract setting. There are no numbered equations. Numerous exercises interspersed in the text encourage readers to test their understanding of new concepts and techniques as they are presented. Detailed solutions of the exercises, included at the back of the book, both serve as models for students and facilitate independent study. Supplementary exercises at the ends of sections, not solved in the book, provide an additional teaching tool.This second edition of Invitation to Complex Analysis has been painstakingly revised by the author's son, himself an award-winning mathematical expositor.

Expanding the Frontiers of Visual Analytics and Visualization

Expanding the Frontiers of Visual Analytics and Visualization Author John Dill
ISBN-10 9781447128045
Year 2012-04-17
Pages 531
Language en
Publisher Springer Science & Business Media
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The field of computer graphics combines display hardware, software, and interactive techniques in order to display and interact with data generated by applications. Visualization is concerned with exploring data and information graphically in such a way as to gain information from the data and determine significance. Visual analytics is the science of analytical reasoning facilitated by interactive visual interfaces. Expanding the Frontiers of Visual Analytics and Visualization provides a review of the state of the art in computer graphics, visualization, and visual analytics by researchers and developers who are closely involved in pioneering the latest advances in the field. It is a unique presentation of multi-disciplinary aspects in visualization and visual analytics, architecture and displays, augmented reality, the use of color, user interfaces and cognitive aspects, and technology transfer. It provides readers with insights into the latest developments in areas such as new displays and new display processors, new collaboration technologies, the role of visual, multimedia, and multimodal user interfaces, visual analysis at extreme scale, and adaptive visualization.

Understanding Analysis

Understanding Analysis Author Stephen Abbott
ISBN-10 9781493927128
Year 2015-05-19
Pages 312
Language en
Publisher Springer
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This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.