Complex Numbers In N Dimensions

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Complex Numbers In N Dimensions

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Author : S. Olariu
language : en
Publisher: Elsevier
Release Date : 2002-06-20

Complex Numbers In N Dimensions written by S. Olariu and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-20 with Mathematics categories.

Two distinct systems of hypercomplex numbers in n dimensions are introduced in this book, for which the multiplication is associative and commutative, and which are rich enough in properties such that exponential and trigonometric forms exist and the concepts of analytic n-complex function, contour integration and residue can be defined.The first type of hypercomplex numbers, called polar hypercomplex numbers, is characterized by the presence in an even number of dimensions greater or equal to 4 of two polar axes, and by the presence in an odd number of dimensions of one polar axis. The other type of hypercomplex numbers exists as a distinct entity only when the number of dimensions n of the space is even, and since the position of a point is specified with the aid of n/2-1 planar angles, these numbers have been called planar hypercomplex numbers.The development of the concept of analytic functions of hypercomplex variables was rendered possible by the existence of an exponential form of the n-complex numbers. Azimuthal angles, which are cyclic variables, appear in these forms at the exponent, and lead to the concept of n-dimensional hypercomplex residue. Expressions are given for the elementary functions of n-complex variable. In particular, the exponential function of an n-complex number is expanded in terms of functions called in this book n-dimensional cosexponential functionsof the polar and respectively planar type, which are generalizations to n dimensions of the sine, cosine and exponential functions.In the case of polar complex numbers, a polynomial can be written as a product of linear or quadratic factors, although it is interesting that several factorizations are in general possible. In the case of planar hypercomplex numbers, a polynomial can always be written as a product of linear factors, although, again, several factorizations are in general possible.The book presents a detailed analysis of the hypercomplex numbers in 2, 3 and 4 dimensions, then presents the properties of hypercomplex numbers in 5 and 6 dimensions, and it continues with a detailed analysis of polar and planar hypercomplex numbers in n dimensions. The essence of this book is the interplay between the algebraic, the geometric and the analytic facets of the relations.

Holomorphic Functions In The Plane And N Dimensional Space

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Author : Klaus Gürlebeck
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-16

Holomorphic Functions In The Plane And N Dimensional Space written by Klaus Gürlebeck 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 2007-11-16 with Mathematics categories.

Complex analysis nowadays has higher-dimensional analoga: the algebra of complex numbers is replaced then by the non-commutative algebra of real quaternions or by Clifford algebras. During the last 30 years the so-called quaternionic and Clifford or hypercomplex analysis successfully developed to a powerful theory with many applications in analysis, engineering and mathematical physics. This textbook introduces both to classical and higher-dimensional results based on a uniform notion of holomorphy. Historical remarks, lots of examples, figures and exercises accompany each chapter.

Visual Complex Analysis

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Author : Tristan Needham
language : en
Publisher: Oxford University Press
Release Date : 1997

Visual Complex Analysis written by Tristan Needham and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

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.

High Dimensional Neurocomputing

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Author : Bipin Kumar Tripathi
language : en
Publisher: Springer
Release Date : 2014-11-05

High Dimensional Neurocomputing written by Bipin Kumar Tripathi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-11-05 with Technology & Engineering categories.

The book presents a coherent understanding of computational intelligence from the perspective of what is known as "intelligent computing" with high-dimensional parameters. It critically discusses the central issue of high-dimensional neurocomputing, such as quantitative representation of signals, extending the dimensionality of neuron, supervised and unsupervised learning and design of higher order neurons. The strong point of the book is its clarity and ability of the underlying theory to unify our understanding of high-dimensional computing where conventional methods fail. The plenty of application oriented problems are presented for evaluating, monitoring and maintaining the stability of adaptive learning machine. Author has taken care to cover the breadth and depth of the subject, both in the qualitative as well as quantitative way. The book is intended to enlighten the scientific community, ranging from advanced undergraduates to engineers, scientists and seasoned researchers in computational intelligence.

The Biggest Ideas In The Universe 2

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Author : Sean Carroll
language : en
Publisher: Simon and Schuster
Release Date : 2024-05-30

The Biggest Ideas In The Universe 2 written by Sean Carroll and has been published by Simon and Schuster this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-30 with Science categories.

THE NEW YORK TIMES BESTSELLER ‘Neat, and extremely simple: only a deep thinker such as Sean Carroll could introduce the complexity of Einstein’s general relativity in such a luminous and straightforward manner.’ Carlo Rovelli, author of Seven Brief Lessons on Physics Immense, strange and infinite, the world of modern physics often feels impenetrable to the undiscerning eye – a jumble of muons, gluons and quarks, impossible to explain without several degrees and a research position at CERN. But it doesn’t have to be this way! Allow world-renowned theoretical physicist and bestselling author Sean Carroll to guide you through the biggest ideas in the universe. Elegant and simple, Carroll unravels a web of theory to get to the heart of the truths they represent about the world around us. — In Quanta and Fields, the second in this landmark trilogy, Carroll delves into the baffling and beautiful world of quantum mechanics. From Schrödinger to Feynman, Carroll travels through the quantum revolution with the greatest minds of the twentieth century. Exploring how several decades of research overturned centuries of convention, Carroll provides a dazzling tour of the most exciting ideas in modern science.

Mathematical Thought From Ancient To Modern Times Volume 3

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Author : Morris Kline
language : en
Publisher: Oxford University Press
Release Date : 1990-03-01

Mathematical Thought From Ancient To Modern Times Volume 3 written by Morris Kline and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-03-01 with Mathematics categories.

This comprehensive history traces the development of mathematical ideas and the careers of the men responsible for them. Volume 1 looks at the disciplines origins in Babylon and Egypt, the creation of geometry and trigonometry by the Greeks, and the role of mathematics in the medieval and early modern periods. Volume 2 focuses on calculus, the rise of analysis in the 19th century, and the number theories of Dedekind and Dirichlet. The concluding volume covers the revival of projective geometry, the emergence of abstract algebra, the beginnings of topology, and the influence of Godel on recent mathematical study.

The Linear Functions Of A Complex Variable

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Author : Frank Nelson Cole
language : en
Publisher:
Release Date : 1890

The Linear Functions Of A Complex Variable written by Frank Nelson Cole and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1890 with Functions categories.

Quanta And Fields

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Author : Sean Carroll
language : en
Publisher: Penguin
Release Date : 2024-05-14

Quanta And Fields written by Sean Carroll and has been published by Penguin this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-05-14 with Science categories.

The instant New York Times bestseller Quanta and Fields, the second book of Sean Carroll’s already internationally acclaimed series The Biggest Ideas in the Universe, is an adventure into the bare stuff of reality. Sean Carroll is creating a profoundly new approach to sharing physics with a broad audience, one that goes beyond analogies to show how physicists really think. He cuts to the bare mathematical essence of our most profound theories, explaining every step in a uniquely accessible way. Quantum field theory is how modern physics describes nature at its most profound level. Starting with the basics of quantum mechanics itself, Sean Carroll explains measurement and entanglement before explaining how the world is really made of fields. You will finally understand why matter is solid, why there is antimatter, where the sizes of atoms come from, and why the predictions of quantum field theory are so spectacularly successful. Fundamental ideas like spin, symmetry, Feynman diagrams, and the Higgs mechanism are explained for real, not just through amusing stories. Beyond Newton, beyond Einstein, and all the intuitive notions that have guided homo sapiens for millennia, this book is a journey to a once unimaginable truth about what our universe is.

Nasa Technical Report

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Author : United States. National Aeronautics and Space Administration
language : en
Publisher:
Release Date : 1973

Nasa Technical Report written by United States. National Aeronautics and Space Administration and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Aerodynamics categories.

Geometrical Methods Of Mathematical Physics

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Author : Bernard F. Schutz
language : en
Publisher: Cambridge University Press
Release Date : 1980-01-28

Geometrical Methods Of Mathematical Physics written by Bernard F. Schutz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-28 with Science categories.

In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.