Visual Complex Functions

Author : Elias Wegert
Publisher : Springer Science & Business Media
ISBN 13 : 3034801807
Total Pages : 360 pages
Book Rating : 4.05/5 ( download)

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Download or read book Visual Complex Functions written by Elias Wegert and published by Springer Science & Business Media. This book was released on 2012-08-30 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Tristan Needham
Publisher : Oxford University Press
ISBN 13 : 9780198534464
Total Pages : 620 pages
Book Rating : 4.69/5 ( download)

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Download or read book Visual Complex Analysis written by Tristan Needham and published by Oxford University Press. This book was released on 1997 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Reinhold Remmert
Publisher : Springer Science & Business Media
ISBN 13 : 1461209390
Total Pages : 464 pages
Book Rating : 4.93/5 ( download)

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Download or read book Theory of Complex Functions written by Reinhold Remmert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Serge Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1475718713
Total Pages : 380 pages
Book Rating : 4.13/5 ( download)

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Download or read book Complex Analysis written by Serge Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Richard A. Silverman
Publisher : Courier Corporation
ISBN 13 : 0486318524
Total Pages : 402 pages
Book Rating : 4.23/5 ( download)

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Download or read book Introductory Complex Analysis written by Richard A. Silverman and published by Courier Corporation. This book was released on 2013-04-15 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shorter version of Markushevich's Theory of Functions of a Complex Variable, appropriate for advanced undergraduate and graduate courses in complex analysis. More than 300 problems, some with hints and answers. 1967 edition.

Author : Elias M. Stein
Publisher : Princeton University Press
ISBN 13 : 1400831156
Total Pages : 398 pages
Book Rating : 4.59/5 ( download)

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Download or read book Complex Analysis written by Elias M. Stein and published by Princeton University Press. This book was released on 2010-04-22 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Michael A. Brilleslyper
Publisher : American Mathematical Soc.
ISBN 13 : 1614441081
Total Pages : 373 pages
Book Rating : 4.83/5 ( download)

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Download or read book Explorations in Complex Analysis written by Michael A. Brilleslyper and published by American Mathematical Soc.. This book was released on 2012-12-31 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hans Schwerdtfeger
Publisher : Courier Corporation
ISBN 13 : 0486135861
Total Pages : 224 pages
Book Rating : 4.61/5 ( download)

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Download or read book Geometry of Complex Numbers written by Hans Schwerdtfeger and published by Courier Corporation. This book was released on 2012-05-23 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: Illuminating, widely praised book on analytic geometry of circles, the Moebius transformation, and 2-dimensional non-Euclidean geometries.

Author : Ahlfors Lars V
Publisher :
ISBN 13 :
Total Pages : 331 pages
Book Rating : 4.98/5 ( download)

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Download or read book Complex Analysis: an Introduction to Theory of Analytic Functions of One Complex Variable written by Ahlfors Lars V and published by . This book was released on 1981 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Roger Penrose
Publisher : Vintage
ISBN 13 : 0593315308
Total Pages : 1136 pages
Book Rating : 4.09/5 ( download)

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Download or read book The Road to Reality written by Roger Penrose and published by Vintage. This book was released on 2021-06-09 with total page 1136 pages. Available in PDF, EPUB and Kindle. Book excerpt: **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