Visual Complex Analysis

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Visual Complex Analysis

Tristan Needham
Visual Complex Analysis Book PDF

Author : Tristan Needham
Publisher : Oxford University Press
Page : 620 pages
File Size : 49,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0198534469

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Visual Complex Analysis by Tristan Needham Pdf

This radical first course on complex analysis brings a beautiful and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. Aimed at undergraduate students in mathematics, physics, and engineering, the book's intuitive explanations, lack of advanced prerequisites, and consciously user-friendly prose style will help students to master the subject more readily than was previously possible. The key to this is the book's use of new geometric arguments in place of the standard calculational ones. These geometric arguments are communicated with the aid of hundreds of diagrams of a standard seldom encountered in mathematical works. A new approach to a classical topic, this work will be of interest to students in mathematics, physics, and engineering, as well as to professionals in these fields.

Visual Complex Functions

Elias Wegert
Visual Complex Functions Book PDF

Author : Elias Wegert
Publisher : Springer Science & Business Media
Page : 374 pages
File Size : 48,6 Mb
Release : 2012-08-30
Category : Mathematics
ISBN : 9783034801805

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Visual Complex Functions by Elias Wegert Pdf

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

Serge Lang
Complex Analysis Book PDF

Author : Serge Lang
Publisher : Springer Science & Business Media
Page : 380 pages
File Size : 40,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781475718713

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Complex Analysis by Serge Lang Pdf

The present book is meant as a text for a course on complex analysis at the advanced undergraduate level, or first-year graduate level. Somewhat more material has been included than can be covered at leisure in one term, to give opportunities for the instructor to exercise his taste, and lead the course in whatever direction strikes his fancy at the time. A large number of routine exercises are included for the more standard portions, and a few harder exercises of striking theoretical interest are also included, but may be omitted in courses addressed to less advanced students. In some sense, I think the classical German prewar texts were the best (Hurwitz-Courant, Knopp, Bieberbach, etc. ) and I would recom mend to anyone to look through them. More recent texts have empha sized connections with real analysis, which is important, but at the cost of exhibiting succinctly and clearly what is peculiar about complex anal ysis: the power series expansion, the uniqueness of analytic continuation, and the calculus of residues. The systematic elementary development of formal and convergent power series was standard fare in the German texts, but only Cartan, in the more recent books, includes this material, which I think is quite essential, e. g. , for differential equations. I have written a short text, exhibiting these features, making it applicable to a wide variety of tastes. The book essentially decomposes into two parts.

Visual Differential Geometry and Forms

Tristan Needham
Visual Differential Geometry and Forms Book PDF

Author : Tristan Needham
Publisher : Princeton University Press
Page : 530 pages
File Size : 53,6 Mb
Release : 2021-07-13
Category : Mathematics
ISBN : 9780691203706

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Visual Differential Geometry and Forms by Tristan Needham Pdf

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.

Visual Group Theory

Nathan Carter
Visual Group Theory Book PDF

Author : Nathan Carter
Publisher : American Mathematical Soc.
Page : 295 pages
File Size : 52,8 Mb
Release : 2021-06-08
Category : Education
ISBN : 9781470464332

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Visual Group Theory by Nathan Carter Pdf

Recipient of the Mathematical Association of America's Beckenbach Book Prize in 2012! 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.

Complex Analysis

Elias M. Stein,Rami Shakarchi
Complex Analysis Book PDF

Author : Elias M. Stein,Rami Shakarchi
Publisher : Princeton University Press
Page : 398 pages
File Size : 55,7 Mb
Release : 2010-04-22
Category : Mathematics
ISBN : 9781400831159

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Complex Analysis by Elias M. Stein,Rami Shakarchi Pdf

With this second volume, we enter the intriguing world of complex analysis. From the first theorems on, the elegance and sweep of the results is evident. The starting point is the simple idea of extending a function initially given for real values of the argument to one that is defined when the argument is complex. From there, one proceeds to the main properties of holomorphic functions, whose proofs are generally short and quite illuminating: the Cauchy theorems, residues, analytic continuation, the argument principle. With this background, the reader is ready to learn a wealth of additional material connecting the subject with other areas of mathematics: the Fourier transform treated by contour integration, the zeta function and the prime number theorem, and an introduction to elliptic functions culminating in their application to combinatorics and number theory. Thoroughly developing a subject with many ramifications, while striking a careful balance between conceptual insights and the technical underpinnings of rigorous analysis, Complex Analysis will be welcomed by students of mathematics, physics, engineering and other sciences. The Princeton Lectures in Analysis represents a sustained effort to introduce the core areas of mathematical analysis while also illustrating the organic unity between them. Numerous examples and applications throughout its four planned volumes, of which Complex Analysis is the second, highlight the far-reaching consequences of certain ideas in analysis to other fields of mathematics and a variety of sciences. Stein and Shakarchi move from an introduction addressing Fourier series and integrals to in-depth considerations of complex analysis; measure and integration theory, and Hilbert spaces; and, finally, further topics such as functional analysis, distributions and elements of probability theory.

Introduction to Complex Analysis

H. A. Priestley
Introduction to Complex Analysis Book PDF

Author : H. A. Priestley
Publisher : OUP Oxford
Page : 344 pages
File Size : 50,7 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 9780191037207

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Introduction to Complex Analysis by H. A. Priestley Pdf

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.

A Course in Complex Analysis

Saeed Zakeri
A Course in Complex Analysis Book PDF

Author : Saeed Zakeri
Publisher : Princeton University Press
Page : 442 pages
File Size : 51,5 Mb
Release : 2021-11-02
Category : Mathematics
ISBN : 9780691207582

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A Course in Complex Analysis by Saeed Zakeri Pdf

"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"--

Interactive Visual Data Analysis

Christian Tominski,Heidrun Schumann
Interactive Visual Data Analysis Book PDF

Author : Christian Tominski,Heidrun Schumann
Publisher : CRC Press
Page : 365 pages
File Size : 51,6 Mb
Release : 2020-04-01
Category : Computers
ISBN : 9781498753999

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Interactive Visual Data Analysis by Christian Tominski,Heidrun Schumann Pdf

Based on comprehensive taxonomies for both data and tasks Considers three challenging problems: incremental visualization, visual design and guidance Systematically investigates the visualization of multi-faceted data and networks A comprehensive overview on interaction is provided Visualization approaches in innovative display environments (large high-resolution displays, smart environments) are discussed

Complex Analysis

Eberhard Freitag,Rolf Busam
Complex Analysis Book PDF

Author : Eberhard Freitag,Rolf Busam
Publisher : Springer Science & Business Media
Page : 553 pages
File Size : 46,9 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783540308232

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Complex Analysis by Eberhard Freitag,Rolf Busam Pdf

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

Explorations in Complex Analysis

Michael A. Brilleslyper,Michael J. Dorff,Jane M. McDougall,James S. Rolf,Lisbeth E. Schaubroeck
Explorations in Complex Analysis Book PDF

Author : Michael A. Brilleslyper,Michael J. Dorff,Jane M. McDougall,James S. Rolf,Lisbeth E. Schaubroeck
Publisher : American Mathematical Soc.
Page : 373 pages
File Size : 40,7 Mb
Release : 2012-12-31
Category : Mathematics
ISBN : 9781614441083

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Explorations in Complex Analysis by Michael A. Brilleslyper,Michael J. Dorff,Jane M. McDougall,James S. Rolf,Lisbeth E. Schaubroeck Pdf

Research topics in the book include complex dynamics, minimal surfaces, fluid flows, harmonic, conformal, and polygonal mappings, and discrete complex analysis via circle packing. The nature of this book is different from many mathematics texts: the focus is on student-driven and technology-enhanced investigation. Interlaced in the reading for each chapter are examples, exercises, explorations, and projects, nearly all linked explicitly with computer applets for visualization and hands-on manipulation.

The Road to Reality

Roger Penrose
The Road to Reality Book PDF

Author : Roger Penrose
Publisher : Vintage
Page : 1136 pages
File Size : 42,8 Mb
Release : 2021-06-09
Category : Science
ISBN : 9780593315309

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The Road to Reality by Roger Penrose Pdf

**WINNER OF THE 2020 NOBEL PRIZE IN PHYSICS** The Road to Reality is the most important and ambitious work of science for a generation. It provides nothing less than a comprehensive account of the physical universe and the essentials of its underlying mathematical theory. It assumes no particular specialist knowledge on the part of the reader, so that, for example, the early chapters give us the vital mathematical background to the physical theories explored later in the book. Roger Penrose's purpose is to describe as clearly as possible our present understanding of the universe and to convey a feeling for its deep beauty and philosophical implications, as well as its intricate logical interconnections. The Road to Reality is rarely less than challenging, but the book is leavened by vivid descriptive passages, as well as hundreds of hand-drawn diagrams. In a single work of colossal scope one of the world's greatest scientists has given us a complete and unrivalled guide to the glories of the universe that we all inhabit. 'Roger Penrose is the most important physicist to work in relativity theory except for Einstein. He is one of the very few people I've met in my life who, without reservation, I call a genius' Lee Smolin

Real Analysis

N. L. Carothers
Real Analysis Book PDF

Author : N. L. Carothers
Publisher : Cambridge University Press
Page : 420 pages
File Size : 53,9 Mb
Release : 2000-08-15
Category : Mathematics
ISBN : 0521497566

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Real Analysis by N. L. Carothers Pdf

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

An Introduction to Complex Analysis

Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas
An Introduction to Complex Analysis Book PDF

Author : Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 45,6 Mb
Release : 2011-07-01
Category : Mathematics
ISBN : 9781461401957

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An Introduction to Complex Analysis by Ravi P. Agarwal,Kanishka Perera,Sandra Pinelas Pdf

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.

Complex Made Simple

David C. Ullrich
Complex Made Simple Book PDF

Author : David C. Ullrich
Publisher : American Mathematical Soc.
Page : 506 pages
File Size : 47,8 Mb
Release : 2008
Category : Functions of complex variables
ISBN : 9780821844793

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Complex Made Simple by David C. Ullrich Pdf

Presents 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. This book is suitable for a first-year course in complex analysis