Non Regular Differential Equations And Calculations Of Electromagnetic Fields

Author : N. E. Tovmasyan,L. Z. Gevorkyan,M. S. Ginovyan,M. N. Bobrova
Publisher : World Scientific
Page : 250 pages
File Size : 41,9 Mb
Release : 1998
Category : Science
ISBN : 9810233361

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Non-regular Differential Equations and Calculations of Electromagnetic Fields by N. E. Tovmasyan,L. Z. Gevorkyan,M. S. Ginovyan,M. N. Bobrova Pdf

This book deals with the boundary value problems for non-regular partial differential equations in the half-plane. Efficient methods are developed for resolution of boundary value problems for improperly elliptic equations ? based on the theory of analytic functions and functional analysis ? having great theoretical and practical importance. In canonical domains (circle, ellipse, half-plane, etc.) explicit formulas for solutions to Riemann-Hilbert and Dirichlet type problems for improperly elliptic equations are obtained. A new approach is proposed for the investigation of the harmonic oscillations of electromagnetic fields in stratified and non-homogeneous media and for the calculation of capacitors bounded by analytic surfaces. The book can be used by professionals in a wide range of specialities, including mathematics, mechanics, physics and many realms of engineering.

Author : Anonim
Publisher : Elsevier
Page : 412 pages
File Size : 55,7 Mb
Release : 1998-04-28
Category : Science
ISBN : 9780080537696

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Nonlinear Diffusion of Electromagnetic Fields by Anonim Pdf

Nonlinear Diffusion of Electromagnetic Fields covers applications of the phenomena of non-linear diffusion of electromagnetic fields, such as magnetic recording, electromagnetic shielding and non-destructive testing, development of CAD software, and the design of magnetic components in electrical machinery. The material presented has direct applications to the analysis of eddy currents in magnetically nonlinear and hysteretic conductors and to the study of magnetization processes in electrically nonlinear superconductors. This book will provide very valuable technical and scientific information to a broad audience of engineers and researchers who are involved in these diverse areas. Contains extensive use of analytical techniques for the solution of nonlinear problems of electromagnetic field diffusion Simple analytical formulas for surface impedances of nonlinear and hysteretic media Analysis of nonlinear diffusion for linear, circular and elliptical polarizations of electromagnetic fields Novel and extensive analysis of eddy current losses in steel laminations for unidirectional and rotating magnetic fields Preisach approach to the modeling of eddy current hysteresis and superconducting hysteresis Extensive study of nonlinear diffusion in superconductors with gradual resistive transitions (scalar and vertorial problems)

Author : Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek
Publisher : Springer Nature
Page : 585 pages
File Size : 41,6 Mb
Release : 2021-09-27
Category : Mathematics
ISBN : 9783030774936

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Operator Theory and Harmonic Analysis by Alexey N. Karapetyants,Vladislav V. Kravchenko,Elijah Liflyand,Helmuth R. Malonek Pdf

This volume is part of the collaboration agreement between Springer and the ISAAC society. This is the first in the two-volume series originating from the 2020 activities within the international scientific conference "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis" (OTHA), Southern Federal University in Rostov-on-Don, Russia. This volume is focused on general harmonic analysis and its numerous applications. The two volumes cover new trends and advances in several very important fields of mathematics, developed intensively over the last decade. The relevance of this topic is related to the study of complex multiparameter objects required when considering operators and objects with variable parameters.

Author : Alexey Karapetyants,Vladislav Kravchenko,Elijah Liflyand
Publisher : Springer Nature
Page : 475 pages
File Size : 53,8 Mb
Release : 2019-08-28
Category : Mathematics
ISBN : 9783030267483

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Modern Methods in Operator Theory and Harmonic Analysis by Alexey Karapetyants,Vladislav Kravchenko,Elijah Liflyand Pdf

This proceedings volume gathers selected, peer-reviewed papers from the "Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII" (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018. The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant. Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.

Author : Helmut Florian
Publisher : World Scientific
Page : 473 pages
File Size : 40,6 Mb
Release : 2001
Category : Mathematics
ISBN : 9789810247645

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Functional-analytic and Complex Methods, Their Interactions, and Applications to Partial Differential Equations by Helmut Florian Pdf

Functional analysis is not only a tool for unifying mathematical analysis, but it also provides the background for today's rapid development of the theory of partial differential equations. Using concepts of functional analysis, the field of complex analysis has developed methods (such as the theory of generalized analytic functions) for solving very general classes of partial differential equations.This book is aimed at promoting further interactions of functional analysis, partial differential equations, and complex analysis including its generalizations such as Clifford analysis. New interesting problems in the field of partial differential equations concern, for instance, the Dirichlet problem for hyperbolic equations. Applications to mathematical physics address mainly Maxwell's equations, crystal optics, dynamical problems for cusped bars, and conservation laws.

Author : Harry Bateman
Publisher : CUP Archive
Page : 178 pages
File Size : 45,5 Mb
Release : 2018-10-13
Category : History
ISBN : 8210379456XXX

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The mathematical analysis of electrical and optical wave-motion on the basis of Maxwell's equations by Harry Bateman Pdf

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Author : James B. Westgard
Publisher : Springer Science & Business Media
Page : 439 pages
File Size : 55,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461223566

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Electrodynamics: A Concise Introduction by James B. Westgard Pdf

This textbook is intended for advanced undergraduates or beginning graduates. It is based on the notes from courses I have taught at Indiana State University from 1967 to the present. The preparation needed is an introductory calculus-based course in physics and its prerequisite calculus courses. Courses in vector analysis and differential equations are useful but not required, since the text introduces these topics. In writing this book, I tried to keep my own experience as a stu dent in mind and to write the kind of book I liked to read. That goal determined the choice of topics, their order, and the method of presentation. The organization of the book is intended to encourage independent study. Accordingly, I have made every effort to keep the material self-contained, to develop the mathematics as it is needed, and to present new material by building incrementally on preceding material. In organizing the text, I have taken care to give explicit cross references, to show the intermediate steps in calculations, and to give many examples. Provided they are within the mathematical scope of this book, I have preferred elegant mathematical treatments over more ad hoc ones, not only for aesthetic reasons, but because they are often more profound and indicate connections to other branches of physics. I have emphasized physical understanding by presenting mechanical models. This book is organized somewhat differently from the traditional textbook at this level.

Author : Leonard Eyges
Publisher : Courier Corporation
Page : 452 pages
File Size : 53,5 Mb
Release : 2012-06-11
Category : Science
ISBN : 9780486152356

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The Classical Electromagnetic Field by Leonard Eyges Pdf

This excellent text covers a year's course. Topics include vectors D and H inside matter, conservation laws for energy, momentum, invariance, form invariance, covariance in special relativity, and more.

Author : Parry Moon,Domina E. Spencer
Publisher : Springer
Page : 243 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642530609

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Field Theory Handbook by Parry Moon,Domina E. Spencer Pdf

Let us first state exactly what this book is and what it is not. It is a compendium of equations for the physicist and the engineer working with electrostatics, magne tostatics, electric currents, electromagnetic fields, heat flow, gravitation, diffusion, optics, or acoustics. It tabulates the properties of 40 coordinate systems, states the Laplace and Helmholtz equations in each coordinate system, and gives the separation equations and their solutions. But it is not a textbook and it does not cover relativistic and quantum phenomena. The history of classical physics may be regarded as an interplay between two ideas, the concept of action-at-a-distance and the concept of a field. Newton's equation of universal gravitation, for instance, implies action-at-a-distance. The same form of equation was employed by COULOMB to express the force between charged particles. AMPERE and GAUSS extended this idea to the phenomenological action between currents. In 1867, LUDVIG LORENZ formulated electrodynamics as retarded action-at-a-distance. At almost the same time, MAXWELL presented the alternative formulation in terms of fields. In most cases, the field approach has shown itself to be the more powerful.

Author : Pei-bai Zhou
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642503191

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Numerical Analysis of Electromagnetic Fields by Pei-bai Zhou Pdf

Numerical methods for solving boundary value problems have developed rapidly. Knowledge of these methods is important both for engineers and scientists. There are many books published that deal with various approximate methods such as the finite element method, the boundary element method and so on. However, there is no textbook that includes all of these methods. This book is intended to fill this gap. The book is designed to be suitable for graduate students in engineering science, for senior undergraduate students as well as for scientists and engineers who are interested in electromagnetic fields. Objective Numerical calculation is the combination of mathematical methods and field theory. A great number of mathematical concepts, principles and techniques are discussed and many computational techniques are considered in dealing with practical problems. The purpose of this book is to provide students with a solid background in numerical analysis of the field problems. The book emphasizes the basic theories and universal principles of different numerical methods and describes why and how different methods work. Readers will then understand any methods which have not been introduced and will be able to develop their own new methods. Organization Many of the most important numerical methods are covered in this book. All of these are discussed and compared with each other so that the reader has a clear picture of their particular advantage, disadvantage and the relation between each of them. The book is divided into four parts and twelve chapters.

Author : Ronald E Mickens
Publisher : World Scientific
Page : 264 pages
File Size : 45,7 Mb
Release : 2000-03-29
Category : Mathematics
ISBN : 9789814493987

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Applications of Nonstandard Finite Difference Schemes by Ronald E Mickens Pdf

The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter 1 gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection–diffusion–reaction equations that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. Chapter 5 discusses exactness, stability properties, and the symplecticity of various schemes including the conditions for which Runge–Kutta methods are exact. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena. Contents:Nonstandard Finite Difference Schemes (R E Mickens)Nonstandard Methods for Advection–Diffusion–Reaction Equations (H V Kojouharov & B M Chen)Application of Nonstandard Finite Differences to Solve the Wave Equation and Maxwell's Equations (J B Cole)Nonstandard Discretization Methods for Some Biological Models (H Al-Kahby et al.)An Introduction to Numerical Integrators Preserving Physical Properties (M J Gander & R Meyer-Spasche) Readership: Researchers in applied mathematics and in the natural and engineering sciences who wish to apply nonstandard finite difference methods. Keywords:Nonstandard Finite Difference Methods;Advection-Diffusion-Reaction Equations;Wave Equations;Discrete-Time Models;Maxwell Equations;Numerical Integrators;Discrete Dynamics;Nonlinear Differential Equations

Author : Weng Cho Chew,Mei Song Tong,Bin Hu
Publisher : Morgan & Claypool Publishers
Page : 259 pages
File Size : 46,7 Mb
Release : 2009
Category : Elastic waves
ISBN : 9781598291483

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Integral Equation Methods for Electromagnetic and Elastic Waves by Weng Cho Chew,Mei Song Tong,Bin Hu Pdf

Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms

Author : Zijad Haznadar,Željko Štih
Publisher : Unknown
Page : 436 pages
File Size : 42,9 Mb
Release : 2000
Category : Electromagnetic fields
ISBN : UCSD:31822031301286

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Electromagnetic Fields, Waves, and Numerical Methods by Zijad Haznadar,Željko Štih Pdf

Author : Kurt O. Friedrichs
Publisher : American Mathematical Soc.
Page : 145 pages
File Size : 44,8 Mb
Release : 2014-11-12
Category : Mathematics
ISBN : 9781470417116

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Mathematical Methods of Electromagnetic Theory by Kurt O. Friedrichs Pdf

This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in electro- and magnetostatics, and (c) a thorough discussion of the central importance of the conservation of charge. It is suitable for advanced undergraduate students in mathematics and physics with a background in advanced calculus and linear algebra, as well as mechanics and electromagnetics at an undergraduate level. Apart from minor corrections to the text, the notation was updated in this edition to follow the conventions of modern vector calculus. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Author : Donald C. Stinson
Publisher : Prentice Hall
Page : 312 pages
File Size : 45,6 Mb
Release : 1976
Category : Electromagnetism
ISBN : UOM:39076005241406

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Intermediate Mathematics of Electromagnetics by Donald C. Stinson Pdf