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Mathematical Methods in Electromagnetism

Author: M Cessenat

Publisher: World Scientific

Published: 1996-07-13

Total Pages: 396

ISBN-13: 9814525383

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This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach. As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials. Contents:Mathematical Modelling of the Electromagnetic Field in Continuous Media: Maxwell Equations and Constitutive RelationsMathematical Framework for ElectromagnetismStationary Scattering Problems with Bounded ObstaclesWaveguide ProblemsStationary Scattering Problems on Unbounded ObstaclesEvolution ProblemsAppendix — Differential Geometry for ElectromagnetismReferencesIndexNotations Readership: Applied mathematicians. keywords:Electromagnetism;Mathematical Modeling;Maxwell Equations;Variational Methods;Differential Geometry;Hodge Decomposition;Impedance Operators;Calderon Operators;Waveguides;Scattering;Outgoing Waves;Causal Problems “I would recommend it to anyone interested in the analysis or numerical analysis of Maxwell's equations for its up-to-date and extensive treatment of the problem.” SIAM Reviews

Book Synopsis Mathematical Methods in Electromagnetism by : M Cessenat

Download or read book Mathematical Methods in Electromagnetism written by M Cessenat and published by World Scientific. This book was released on 1996-07-13 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach. As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials. Contents:Mathematical Modelling of the Electromagnetic Field in Continuous Media: Maxwell Equations and Constitutive RelationsMathematical Framework for ElectromagnetismStationary Scattering Problems with Bounded ObstaclesWaveguide ProblemsStationary Scattering Problems on Unbounded ObstaclesEvolution ProblemsAppendix — Differential Geometry for ElectromagnetismReferencesIndexNotations Readership: Applied mathematicians. keywords:Electromagnetism;Mathematical Modeling;Maxwell Equations;Variational Methods;Differential Geometry;Hodge Decomposition;Impedance Operators;Calderon Operators;Waveguides;Scattering;Outgoing Waves;Causal Problems “I would recommend it to anyone interested in the analysis or numerical analysis of Maxwell's equations for its up-to-date and extensive treatment of the problem.” SIAM Reviews

Mathematical Methods of Electromagnetic Theory

Author: Kurt O. Friedrichs

Publisher: American Mathematical Soc.

Published: 2014-11-12

Total Pages: 159

ISBN-13: 1470417111

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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.

Book Synopsis Mathematical Methods of Electromagnetic Theory by : Kurt O. Friedrichs

Download or read book Mathematical Methods of Electromagnetic Theory written by Kurt O. Friedrichs and published by American Mathematical Soc.. This book was released on 2014-11-12 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Numerical Methods in Electromagnetism

Author: M. V.K. Chari

Publisher: Academic Press

Published: 2000

Total Pages: 783

ISBN-13: 012615760X

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Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. Numerical Methods in Electromagnetism will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students. Comprehensive descriptions of numerical methods In-depth introduction to finite differences, finite elements, and integral equations Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis Numerical examples to facilitate understanding of the methods Appendices for quick reference of mathematical and numerical methods employed

Book Synopsis Numerical Methods in Electromagnetism by : M. V.K. Chari

Download or read book Numerical Methods in Electromagnetism written by M. V.K. Chari and published by Academic Press. This book was released on 2000 with total page 783 pages. Available in PDF, EPUB and Kindle. Book excerpt: Electromagnetics is the foundation of our electric technology. It describes the fundamental principles upon which electricity is generated and used. This includes electric machines, high voltage transmission, telecommunication, radar, and recording and digital computing. Numerical Methods in Electromagnetism will serve both as an introductory text for graduate students and as a reference book for professional engineers and researchers. This book leads the uninitiated into the realm of numerical methods for solving electromagnetic field problems by examples and illustrations. Detailed descriptions of advanced techniques are also included for the benefit of working engineers and research students. Comprehensive descriptions of numerical methods In-depth introduction to finite differences, finite elements, and integral equations Illustrations and applications of linear and nonlinear solutions for multi-dimensional analysis Numerical examples to facilitate understanding of the methods Appendices for quick reference of mathematical and numerical methods employed

Mathematical Foundations for Electromagnetic Theory

Author: Donald G. Dudley

Publisher: Wiley-IEEE Press

Published: 1994-05-18

Total Pages: 264

ISBN-13: 9780780310223

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Co-published with Oxford University Press. This highly technical and thought-provoking book stresses the development of mathematical foundations for the application of the electromagnetic model to problems of research and technology. Features include in-depth coverage of linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. This book will be of interest graduate-level students in engineering, electromagnetics, physics, and applied mathematics as well as to research engineers, physicists, and scientists.

Book Synopsis Mathematical Foundations for Electromagnetic Theory by : Donald G. Dudley

Download or read book Mathematical Foundations for Electromagnetic Theory written by Donald G. Dudley and published by Wiley-IEEE Press. This book was released on 1994-05-18 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Co-published with Oxford University Press. This highly technical and thought-provoking book stresses the development of mathematical foundations for the application of the electromagnetic model to problems of research and technology. Features include in-depth coverage of linear spaces, Green's functions, spectral expansions, electromagnetic source representations, and electromagnetic boundary value problems. This book will be of interest graduate-level students in engineering, electromagnetics, physics, and applied mathematics as well as to research engineers, physicists, and scientists.

Mathematical Methods For Physics

Author: H. W. Wyld

Publisher: CRC Press

Published: 2018-03-14

Total Pages: 296

ISBN-13: 0429978642

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This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.

Book Synopsis Mathematical Methods For Physics by : H. W. Wyld

Download or read book Mathematical Methods For Physics written by H. W. Wyld and published by CRC Press. This book was released on 2018-03-14 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic book helps students learn the basics in physics by bridging the gap between mathematics and the basic fundamental laws of physics. With supplemental material such as graphs and equations, Mathematical Methods for Physics creates a strong, solid anchor of learning. The text has three parts: Part I focuses on the use of special functions in solving the homogeneous partial differential equations of physics, and emphasizes applications to topics such as electrostatics, wave guides, and resonant cavities, vibrations of membranes, heat flow, potential flow in fluids, plane and spherical waves. Part II deals with the solution of inhomogeneous differential equations with particular emphasis on problems in electromagnetism, Green's functions for Poisson's equation, the wave equation and the diffusion equation, and the solution of integral equations by iteration, eigenfunction expansion and the Fredholm series. Finally, Part II explores complex variable techniques, including evalution of itegrals, dispersion relations, special functions in the complex plane, one-sided Fourier transforms, and Laplace transforms.

Advanced Electromagnetic Wave Propagation Methods

Author: Guillermo Gonzalez

Publisher: CRC Press

Published: 2021-11-16

Total Pages: 719

ISBN-13: 1000476642

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This textbook provides a solid foundation into many approaches that are used in the analysis of advanced electromagnetic wave propagation problems. The techniques discussed are essential to obtain closed-form solutions or asymptotic solutions and meet an existing need for instructors and students in electromagnetic theory. The book covers various advanced mathematical methods used in the evaluation of the electromagnetic fields in rectangular, cylindrical and spherical geometries. The mathematics of special functions (i.e., Bessel, Hankel, Airy, Legendre, Error, etc.) are covered in depth, including appropriate Appendices. The author takes particular care to provide detailed explanations of auxiliary potentials, Hertz’s vectors, Debye potentials, as well as the use of Green functions, the Watson transformation and the method of steepest descent in the solution of electromagnetic problems. Overall, Advanced Electromagnetic Wave Propagation Methods is a good source for the many skills required in obtaining closed form and asymptotic solution, which in many instances cannot be obtained using computer codes of Maxwell’s equations. Thus, it provides an excellent training for preparing graduate students in their research work. This book is intended for a graduate course in electromagnetic theory for students in electrical engineering. Students in physics and professionals will also find it appropriate and useful. Provides a comprehensive and unified treatment of radiation and propagation problems Presents a detailed explanation in the use of Green functions, the Watson transformation and the method of steepest descent as they apply to electromagnetic problems Demonstrates various advanced mathematical techniques used in the evaluation of the electromagnetic fields Details how to formulate and obtain a closed-form solution or an asymptotic solution Includes appendices for Bessel, Legendre, Airy and Error functions

Book Synopsis Advanced Electromagnetic Wave Propagation Methods by : Guillermo Gonzalez

Download or read book Advanced Electromagnetic Wave Propagation Methods written by Guillermo Gonzalez and published by CRC Press. This book was released on 2021-11-16 with total page 719 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a solid foundation into many approaches that are used in the analysis of advanced electromagnetic wave propagation problems. The techniques discussed are essential to obtain closed-form solutions or asymptotic solutions and meet an existing need for instructors and students in electromagnetic theory. The book covers various advanced mathematical methods used in the evaluation of the electromagnetic fields in rectangular, cylindrical and spherical geometries. The mathematics of special functions (i.e., Bessel, Hankel, Airy, Legendre, Error, etc.) are covered in depth, including appropriate Appendices. The author takes particular care to provide detailed explanations of auxiliary potentials, Hertz’s vectors, Debye potentials, as well as the use of Green functions, the Watson transformation and the method of steepest descent in the solution of electromagnetic problems. Overall, Advanced Electromagnetic Wave Propagation Methods is a good source for the many skills required in obtaining closed form and asymptotic solution, which in many instances cannot be obtained using computer codes of Maxwell’s equations. Thus, it provides an excellent training for preparing graduate students in their research work. This book is intended for a graduate course in electromagnetic theory for students in electrical engineering. Students in physics and professionals will also find it appropriate and useful. Provides a comprehensive and unified treatment of radiation and propagation problems Presents a detailed explanation in the use of Green functions, the Watson transformation and the method of steepest descent as they apply to electromagnetic problems Demonstrates various advanced mathematical techniques used in the evaluation of the electromagnetic fields Details how to formulate and obtain a closed-form solution or an asymptotic solution Includes appendices for Bessel, Legendre, Airy and Error functions

Non-linear Electromagnetic Systems

Author: Volkmar Kose

Publisher: IOS Press

Published: 1998

Total Pages: 926

ISBN-13: 9789051993813

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The contents is dominated by the latest problems of applied electrical engineering, micro electromechanics, biosensor technology and biomagnetism. The book covers the numerical calculation methods for the design and optimization of sensors, actuators and electric machines, as well as the treatment of inverse problems, in materials testing and in the field of medicine in particular. Other central topics are the material properties and their simulation and much consideration is given to micro-electromechanics.

Book Synopsis Non-linear Electromagnetic Systems by : Volkmar Kose

Download or read book Non-linear Electromagnetic Systems written by Volkmar Kose and published by IOS Press. This book was released on 1998 with total page 926 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contents is dominated by the latest problems of applied electrical engineering, micro electromechanics, biosensor technology and biomagnetism. The book covers the numerical calculation methods for the design and optimization of sensors, actuators and electric machines, as well as the treatment of inverse problems, in materials testing and in the field of medicine in particular. Other central topics are the material properties and their simulation and much consideration is given to micro-electromechanics.

Mathematical Models and Numerical Simulation in Electromagnetism

Author: Alfredo Bermúdez de Castro

Publisher: Springer

Published: 2014-07-22

Total Pages: 432

ISBN-13: 3319029495

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The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

Book Synopsis Mathematical Models and Numerical Simulation in Electromagnetism by : Alfredo Bermúdez de Castro

Download or read book Mathematical Models and Numerical Simulation in Electromagnetism written by Alfredo Bermúdez de Castro and published by Springer. This book was released on 2014-07-22 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book represents a basic support for a master course in electromagnetism oriented to numerical simulation. The main goal of the book is that the reader knows the boundary-value problems of partial differential equations that should be solved in order to perform computer simulation of electromagnetic processes. Moreover it includes a part devoted to electric circuit theory based on ordinary differential equations. The book is mainly oriented to electric engineering applications, going from the general to the specific, namely, from the full Maxwell’s equations to the particular cases of electrostatics, direct current, magnetostatics and eddy currents models. Apart from standard exercises related to analytical calculus, the book includes some others oriented to real-life applications solved with MaxFEM free simulation software.

Mathematical Methods in Electro-Magneto-Elasticity

Author: Demosthenis I. Bardzokas

Publisher: Springer Science & Business Media

Published: 2007-05-19

Total Pages: 539

ISBN-13: 3540710310

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The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. This book fills many gaps in the theoretical literature which arise due to the complexity of the problem. A vast number of problems are considered so that the reader can get a clear quantitative and qualitative understanding of the phenomena taking place.

Book Synopsis Mathematical Methods in Electro-Magneto-Elasticity by : Demosthenis I. Bardzokas

Download or read book Mathematical Methods in Electro-Magneto-Elasticity written by Demosthenis I. Bardzokas and published by Springer Science & Business Media. This book was released on 2007-05-19 with total page 539 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. This book fills many gaps in the theoretical literature which arise due to the complexity of the problem. A vast number of problems are considered so that the reader can get a clear quantitative and qualitative understanding of the phenomena taking place.

Computational Electromagnetics

Author: Anders Bondeson

Publisher: Springer Science & Business Media

Published: 2005-08-15

Total Pages: 232

ISBN-13: 0387261583

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Describes most popular computational methods used to solve problems in electromagnetics Matlab code is included throughout, so that the reader can implement the various techniques discussed Exercises included

Book Synopsis Computational Electromagnetics by : Anders Bondeson

Download or read book Computational Electromagnetics written by Anders Bondeson and published by Springer Science & Business Media. This book was released on 2005-08-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describes most popular computational methods used to solve problems in electromagnetics Matlab code is included throughout, so that the reader can implement the various techniques discussed Exercises included