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Visual Complex Analysis

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Visual Complex Analysis

Visual Complex Analysis Book
Author : Tristan Needham
Publisher : Oxford University Press
Release : 1998
ISBN : 9780198534464
Language : En, Es, Fr & De

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Book Description :

This radical approach to complex analysis replaces the standard calculational arguments with new geometric ones. Using several hundred diagrams this is a new visual approach to the topic.

Visual Complex Analysis

Visual Complex Analysis Book
Author : Tristan Needham
Publisher : Unknown
Release : 2004
ISBN : 0987650XXX
Language : En, Es, Fr & De

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Book Description :

Download Visual Complex Analysis book written by Tristan Needham, available in PDF, EPUB, and Kindle, or read full book online anywhere and anytime. Compatible with any devices.

Visual complex analysis

                                                                        Visual complex analysis Book
Author : Anonim
Publisher : Unknown
Release : 2007
ISBN : 9787115155160
Language : En, Es, Fr & De

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Book Description :

本书介绍了几何、复变函数变换、默比乌斯变换、微分、非欧几何、复积分、柯西公式、向量场、复积分、调和函数等内容。

Visual Differential Geometry and Forms

Visual Differential Geometry and Forms Book
Author : Tristan Needham
Publisher : Princeton University Press
Release : 2021-07-13
ISBN : 0691203709
Language : En, Es, Fr & De

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Book Description :

An inviting, intuitive, and visual exploration of differential geometry and forms Visual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner. Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book. Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.

Introduction to Complex Analysis

Introduction to Complex Analysis Book
Author : H. A. Priestley
Publisher : OUP Oxford
Release : 2003-08-28
ISBN : 0191037206
Language : En, Es, Fr & De

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Book Description :

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.

Complex Analysis

Complex Analysis Book
Author : John M. Howie
Publisher : Springer Science & Business Media
Release : 2012-12-06
ISBN : 1447100271
Language : En, Es, Fr & De

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Book Description :

Complex analysis can be a difficult subject and many introductory texts are just too ambitious for today’s students. This book takes a lower starting point than is traditional and concentrates on explaining the key ideas through worked examples and informal explanations, rather than through "dry" theory.

Geometry of Complex Numbers

Geometry of Complex Numbers Book
Author : Hans Schwerdtfeger
Publisher : Courier Corporation
Release : 2012-05-23
ISBN : 0486135861
Language : En, Es, Fr & De

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Book Description :

Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Complex Made Simple

Complex Made Simple Book
Author : David C. Ullrich
Publisher : American Mathematical Soc.
Release : 2008
ISBN : 0821844792
Language : En, Es, Fr & De

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Book Description :

Perhaps uniquely among mathematical topics, complex analysis presents the student with the opportunity to learn a thoroughly developed subject that is rich in both theory and applications. Even in an introductory course, the theorems and techniques can have elegant formulations. But for any of these profound results, the student is often left asking: What does it really mean? Where does it come from? In Complex Made Simple, David Ullrich shows the student how to think like an analyst. In many cases, results are discovered or derived, with an explanation of how the students might have found the theorem on their own. Ullrich explains why a proof works. He will also, sometimes, explain why a tempting idea does not work. Complex Made Simple looks at the Dirichlet problem for harmonic functions twice: once using the Poisson integral for the unit disk and again in an informal section on Brownian motion, where the reader can understand intuitively how the Dirichlet problem works for general domains.Ullrich also takes considerable care to discuss the modular group, modular function, and covering maps, which become important ingredients in his modern treatment of the often-overlooked original proof of the Big Picard Theorem. This book is suitable for a first-year course in complex analysis. The exposition is aimed directly at the students, with plenty of details included. The prerequisite is a good course in advanced calculus or undergraduate analysis.

Function Theory of One Complex Variable

Function Theory of One Complex Variable Book
Author : Robert Everist Greene,Steven George Krantz
Publisher : American Mathematical Soc.
Release : 2006
ISBN : 9780821839621
Language : En, Es, Fr & De

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Book Description :

Complex analysis is one of the most central subjects in mathematics. It is compelling and rich in its own right, but it is also remarkably useful in a wide variety of other mathematical subjects, both pure and applied. This book is different from others in that it treats complex variables as a direct development from multivariable real calculus. As each new idea is introduced, it is related to the corresponding idea from real analysis and calculus. The text is rich with examples and exercises that illustrate this point. The authors have systematically separated the analysis from the topology, as can be seen in their proof of the Cauchy theorem. The book concludes with several chapters on special topics, including full treatments of special functions, the prime number theorem, and the Bergman kernel. The authors also treat $H^p$ spaces and Painleve's theorem on smoothness to the boundary for conformal maps. This book is a text for a first-year graduate course in complex analysis. It is an engaging and modern introduction to the subject, reflecting the authors' expertise both as mathematicians and as expositors.

A Complex Analysis Problem Book

A Complex Analysis Problem Book Book
Author : Daniel Alpay
Publisher : Birkhäuser
Release : 2016-10-26
ISBN : 3319421816
Language : En, Es, Fr & De

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Book Description :

This second edition presents a collection of exercises on the theory of analytic functions, including completed and detailed solutions. It introduces students to various applications and aspects of the theory of analytic functions not always touched on in a first course, while also addressing topics of interest to electrical engineering students (e.g., the realization of rational functions and its connections to the theory of linear systems and state space representations of such systems). It provides examples of important Hilbert spaces of analytic functions (in particular the Hardy space and the Fock space), and also includes a section reviewing essential aspects of topology, functional analysis and Lebesgue integration. Benefits of the 2nd edition Rational functions are now covered in a separate chapter. Further, the section on conformal mappings has been expanded.

A Course in Complex Analysis

A Course in Complex Analysis Book
Author : Saeed Zakeri
Publisher : Princeton University Press
Release : 2021-10-12
ISBN : 0691207585
Language : En, Es, Fr & De

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Book Description :

"This textbook is intended for a year-long graduate course on complex analysis, a branch of mathematical analysis that has broad applications, particularly in physics, engineering, and applied mathematics. Based on nearly twenty years of classroom lectures, the book is accessible enough for independent study, while the rigorous approach will appeal to more experienced readers and scholars, propelling further research in this field. While other graduate-level complex analysis textbooks do exist, Zakeri takes a distinctive approach by highlighting the geometric properties and topological underpinnings of this area. Zakeri includes more than three hundred and fifty problems, with problem sets at the end of each chapter, along with additional solved examples. Background knowledge of undergraduate analysis and topology is needed, but the thoughtful examples are accessible to beginning graduate students and advanced undergraduates. At the same time, the book has sufficient depth for advanced readers to enhance their own research. The textbook is well-written, clearly illustrated, and peppered with historical information, making it approachable without sacrificing rigor. It is poised to be a valuable textbook for graduate students, filling a needed gap by way of its level and unique approach"--

A Geometric Approach to Differential Forms

A Geometric Approach to Differential Forms Book
Author : David Bachman
Publisher : Springer Science & Business Media
Release : 2012-02-02
ISBN : 0817683046
Language : En, Es, Fr & De

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Book Description :

This text presents differential forms from a geometric perspective accessible at the undergraduate level. It begins with basic concepts such as partial differentiation and multiple integration and gently develops the entire machinery of differential forms. The subject is approached with the idea that complex concepts can be built up by analogy from simpler cases, which, being inherently geometric, often can be best understood visually. Each new concept is presented with a natural picture that students can easily grasp. Algebraic properties then follow. The book contains excellent motivation, numerous illustrations and solutions to selected problems.

Complex Analysis with MATHEMATICA

Complex Analysis with MATHEMATICA   Book
Author : William T. Shaw
Publisher : Cambridge University Press
Release : 2006-04-20
ISBN : 0521836263
Language : En, Es, Fr & De

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Book Description :

This book presents a way of learning complex analysis, using Mathematica. Includes CD with electronic version of the book.

Complex Variables

Complex Variables Book
Author : Stephen D. Fisher
Publisher : Courier Corporation
Release : 2012-04-25
ISBN : 0486134849
Language : En, Es, Fr & De

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Book Description :

Topics include the complex plane, basic properties of analytic functions, analytic functions as mappings, analytic and harmonic functions in applications, transform methods. Hundreds of solved examples, exercises, applications. 1990 edition. Appendices.

Interactive Visual Data Analysis

Interactive Visual Data Analysis Book
Author : Christian Tominski,Heidrun Schumann
Publisher : CRC Press
Release : 2020-03-27
ISBN : 1351648748
Language : En, Es, Fr & De

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Book Description :

In the age of big data, being able to make sense of data is an important key to success. Interactive Visual Data Analysis advocates the synthesis of visualization, interaction, and automatic computation to facilitate insight generation and knowledge crystallization from large and complex data. The book provides a systematic and comprehensive overview of visual, interactive, and analytical methods. It introduces criteria for designing interactive visual data analysis solutions, discusses factors influencing the design, and examines the involved processes. The reader is made familiar with the basics of visual encoding and gets to know numerous visualization techniques for multivariate data, temporal data, geo-spatial data, and graph data. A dedicated chapter introduces general concepts for interacting with visualizations and illustrates how modern interaction technology can facilitate the visual data analysis in many ways. Addressing today’s large and complex data, the book covers relevant automatic analytical computations to support the visual data analysis. The book also sheds light on advanced concepts for visualization in multi-display environments, user guidance during the data analysis, and progressive visual data analysis. The authors present a top-down perspective on interactive visual data analysis with a focus on concise and clean terminology. Many real-world examples and rich illustrations make the book accessible to a broad interdisciplinary audience from students, to experts in the field, to practitioners in data-intensive application domains. Features: Dedicated to the synthesis of visual, interactive, and analysis methods Systematic top-down view on visualization, interaction, and automatic analysis Broad coverage of fundamental and advanced visualization techniques Comprehensive chapter on interacting with visual representations Extensive integration of automatic computational methods Accessible portrayal of cutting-edge visual analytics technology Foreword by Jack van Wijk For more information, you can also visit the author website, where the book's figures will be made available under the CC BY Open Access license: https://ivda-book.de/

Visual Group Theory

Visual Group Theory Book
Author : Nathan Carter
Publisher : American Mathematical Soc.
Release : 2009-12-31
ISBN : 088385757X
Language : En, Es, Fr & De

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Book Description :

Group theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory.

Real Analysis

Real Analysis Book
Author : N. L. Carothers
Publisher : Cambridge University Press
Release : 2000-08-15
ISBN : 9780521497565
Language : En, Es, Fr & De

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Book Description :

A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.

Differential Geometry of Curves and Surfaces

Differential Geometry of Curves and Surfaces Book
Author : Kristopher Tapp
Publisher : Springer
Release : 2016-09-30
ISBN : 3319397990
Language : En, Es, Fr & De

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Book Description :

This is a textbook on differential geometry well-suited to a variety of courses on this topic. For readers seeking an elementary text, the prerequisites are minimal and include plenty of examples and intermediate steps within proofs, while providing an invitation to more excursive applications and advanced topics. For readers bound for graduate school in math or physics, this is a clear, concise, rigorous development of the topic including the deep global theorems. For the benefit of all readers, the author employs various techniques to render the difficult abstract ideas herein more understandable and engaging. Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships. Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut’s Theorem is presented as a conservation law for angular momentum. Green’s Theorem makes possible a drafting tool called a planimeter. Foucault’s Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface. In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn’t work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.

The Shape of Space

The Shape of Space Book
Author : Jeffrey R. Weeks
Publisher : CRC Press
Release : 2001-12-12
ISBN : 1135542651
Language : En, Es, Fr & De

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Book Description :

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

Complex Analysis

Complex Analysis Book
Author : Theodore W. Gamelin
Publisher : Springer Science & Business Media
Release : 2013-11-01
ISBN : 0387216073
Language : En, Es, Fr & De

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Book Description :

An introduction to complex analysis for students with some knowledge of complex numbers from high school. It contains sixteen chapters, the first eleven of which are aimed at an upper division undergraduate audience. The remaining five chapters are designed to complete the coverage of all background necessary for passing PhD qualifying exams in complex analysis. Topics studied include Julia sets and the Mandelbrot set, Dirichlet series and the prime number theorem, and the uniformization theorem for Riemann surfaces, with emphasis placed on the three geometries: spherical, euclidean, and hyperbolic. Throughout, exercises range from the very simple to the challenging. The book is based on lectures given by the author at several universities, including UCLA, Brown University, La Plata, Buenos Aires, and the Universidad Autonomo de Valencia, Spain.