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Topological Foundations Of Electromagnetism (Second Edition)

2022-05-30 Science
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Release : 2022-05-30
Genre : Science
Kind : eBook
Book Rating : 315/5 ( reviews)

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Book Synopsis Topological Foundations Of Electromagnetism (Second Edition) by : Terence William Barrett

Download or read book Topological Foundations Of Electromagnetism (Second Edition) written by Terence William Barrett. This book was released on 2022-05-30. Available in PDF, EPUB and Kindle. Book excerpt: The aims of the book are: (1) to extend Maxwell theory to non-Abelian group forms; (2) to demonstrate that the foundations of electromagnetism are topological; (3) to show the multi-disciplinary nature of communications; (4) to demonstrate the effectiveness of modulated signals in penetrating media; (5) to demonstrate that geometric (Clifford) algebra is the appropriate algebra describing modulated signals.The book is important in indicating that the classical theory of electromagnetism, or Maxwell theory, can be developed to address situations and signals of differing symmetry form, and that different topological spaces require that development.

Advanced Electromagnetism

1995 Science
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Release : 1995
Genre : Science
Kind : eBook
Book Rating : 952/5 ( reviews)

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Book Synopsis Advanced Electromagnetism by : Terence William Barrett

Download or read book Advanced Electromagnetism written by Terence William Barrett. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Electromagnetism: Foundations, Theory and Applications treats what is conventionally called electromagnetism or Maxwell's theory within the context of gauge theory or Yang-Mills theory. A major theme of this book is that fields are not stand-alone entities but are defined by their boundary conditions. The book has practical relevance to efficient antenna design, the understanding of forces and stresses in high energy pulses, ring laser gyros, high speed computer logic elements, efficient transfer of power, parametric conversion, and many other devices and systems. Conventional electromagnetism is shown to be an underdeveloped, rather than a completely developed, field of endeavor, with major challenges in development still to be met.

Electromagnetic Theory and Computation

2004-06-14 Mathematics
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Release : 2004-06-14
Genre : Mathematics
Kind : eBook
Book Rating : 607/5 ( reviews)

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Book Synopsis Electromagnetic Theory and Computation by : Paul W. Gross

Download or read book Electromagnetic Theory and Computation written by Paul W. Gross. This book was released on 2004-06-14. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the connection between algebraic structures in topology and computational methods for 3-dimensional electric and magnetic field computation. The connection between topology and electromagnetism has been known since the 19th century, but there has been little exposition of its relevance to computational methods in modern topological language. This book is an effort to close that gap. It will be of interest to people working in finite element methods for electromagnetic computation and those who have an interest in numerical and industrial applications of algebraic topology.

Foundations of Classical Electrodynamics

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 512/5 ( reviews)

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Book Synopsis Foundations of Classical Electrodynamics by : Friedrich W Hehl

Download or read book Foundations of Classical Electrodynamics written by Friedrich W Hehl. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: In this book we display the fundamental structure underlying classical electro dynamics, i. e. , the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector analysis. Some knowledge of differential geometry would help. Our approach rests on the metric-free integral formulation of the conservation laws of electrodynamics in the tradition of F. Kottler (1922), E. Cartan (1923), and D. van Dantzig (1934), and we stress, in particular, the axiomatic point of view. In this manner we are led to an understanding of why the Maxwell equa tions have their specific form. We hope that our book can be seen in the classical tradition of the book by E. J. Post (1962) on the Formal Structure of Electro magnetics and of the chapter "Charge and Magnetic Flux" of the encyclopedia article on classical field theories by C. Truesdell and R. A. Toupin (1960), in cluding R. A. Toupin's Bressanone lectures (1965); for the exact references see the end of the introduction on page 11. .

Mathematical Foundations of Computational Electromagnetism

2018-06-09 Mathematics
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Release : 2018-06-09
Genre : Mathematics
Kind : eBook
Book Rating : 422/5 ( reviews)

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Book Synopsis Mathematical Foundations of Computational Electromagnetism by : Franck Assous

Download or read book Mathematical Foundations of Computational Electromagnetism written by Franck Assous. This book was released on 2018-06-09. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD). These equations and boundary conditions are discussed, including a brief review of absorbing boundary conditions. The focus then moves to well‐posedness results. The relevant function spaces are introduced, with an emphasis on boundary and topological conditions. General variational frameworks are defined for static and quasi-static problems, time-harmonic problems (including fixed frequency or Helmholtz-like problems and unknown frequency or eigenvalue problems), and time-dependent problems, with or without constraints. They are then applied to prove the well-posedness of Maxwell’s equations and their simplified models, in the various settings described above. The book is completed with a discussion of dimensionally reduced models in prismatic and axisymmetric geometries, and a survey of existence and uniqueness results for the Vlasov-Poisson, Vlasov-Maxwell and MHD equations. The book addresses mainly researchers in applied mathematics who work on Maxwell’s equations. However, it can be used for master or doctorate-level courses on mathematical electromagnetism as it requires only a bachelor-level knowledge of analysis.

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