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Differential Forms in Electromagnetics

Author: Ismo V. Lindell

Publisher: John Wiley & Sons

Published: 2004-04-27

Total Pages: 276

ISBN-13: 9780471648017

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An introduction to multivectors, dyadics, and differential forms for electrical engineers While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically. George Deschamps pioneered the application of differential forms to electrical engineering but never completed his work. Now, Ismo V. Lindell, an internationally recognized authority on differential forms, provides a clear and practical introduction to replacing classical Gibbsian vector calculus with the mathematical formalism of differential forms. In Differential Forms in Electromagnetics, Lindell simplifies the notation and adds memory aids in order to ease the reader's leap from Gibbsian analysis to differential forms, and provides the algebraic tools corresponding to the dyadics of Gibbsian analysis that have long been missing from the formalism. He introduces the reader to basic EM theory and wave equations for the electromagnetic two-forms, discusses the derivation of useful identities, and explains novel ways of treating problems in general linear (bi-anisotropic) media. Clearly written and devoid of unnecessary mathematical jargon, Differential Forms in Electromagnetics helps engineers master an area of intense interest for anyone involved in research on metamaterials.

Book Synopsis Differential Forms in Electromagnetics by : Ismo V. Lindell

Download or read book Differential Forms in Electromagnetics written by Ismo V. Lindell and published by John Wiley & Sons. This book was released on 2004-04-27 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to multivectors, dyadics, and differential forms for electrical engineers While physicists have long applied differential forms to various areas of theoretical analysis, dyadic algebra is also the most natural language for expressing electromagnetic phenomena mathematically. George Deschamps pioneered the application of differential forms to electrical engineering but never completed his work. Now, Ismo V. Lindell, an internationally recognized authority on differential forms, provides a clear and practical introduction to replacing classical Gibbsian vector calculus with the mathematical formalism of differential forms. In Differential Forms in Electromagnetics, Lindell simplifies the notation and adds memory aids in order to ease the reader's leap from Gibbsian analysis to differential forms, and provides the algebraic tools corresponding to the dyadics of Gibbsian analysis that have long been missing from the formalism. He introduces the reader to basic EM theory and wave equations for the electromagnetic two-forms, discusses the derivation of useful identities, and explains novel ways of treating problems in general linear (bi-anisotropic) media. Clearly written and devoid of unnecessary mathematical jargon, Differential Forms in Electromagnetics helps engineers master an area of intense interest for anyone involved in research on metamaterials.

Differential Forms on Electromagnetic Networks

Author: N. V. Balasubramanian

Publisher: Elsevier

Published: 2018-01-18

Total Pages: 201

ISBN-13: 1483103242

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Differential Forms on Electromagnetic Networks deals with the use of combinatorial techniques in electrical circuit, machine analysis, and the relationship between circuit quantities and electromagnetic fields. The monograph is also an introduction to the organization of field equations by the methods of differential forms. The book covers topics such as algebraic structural relations in an electric circuit; mesh and node-pair analysis; exterior differential structures; generalized Stoke's theorem and tensor analysis; and Maxwell's electromagnetic equation. Also covered in the book are the applications for the field network model; oscillatory behavior of electric machines; and the rotation tensor in machine differential structures. The text is recommended for engineering students who would like to be familiarized with electromagnetic networks and its related topics.

Book Synopsis Differential Forms on Electromagnetic Networks by : N. V. Balasubramanian

Download or read book Differential Forms on Electromagnetic Networks written by N. V. Balasubramanian and published by Elsevier. This book was released on 2018-01-18 with total page 201 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Forms on Electromagnetic Networks deals with the use of combinatorial techniques in electrical circuit, machine analysis, and the relationship between circuit quantities and electromagnetic fields. The monograph is also an introduction to the organization of field equations by the methods of differential forms. The book covers topics such as algebraic structural relations in an electric circuit; mesh and node-pair analysis; exterior differential structures; generalized Stoke's theorem and tensor analysis; and Maxwell's electromagnetic equation. Also covered in the book are the applications for the field network model; oscillatory behavior of electric machines; and the rotation tensor in machine differential structures. The text is recommended for engineering students who would like to be familiarized with electromagnetic networks and its related topics.

Differential Forms

Author: Steven H. Weintraub

Publisher: Academic Press

Published: 1997

Total Pages: 50

ISBN-13: 9780127425108

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This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student

Book Synopsis Differential Forms by : Steven H. Weintraub

Download or read book Differential Forms written by Steven H. Weintraub and published by Academic Press. This book was released on 1997 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is one of the first to treat vector calculus using differential forms in place of vector fields and other outdated techniques. Geared towards students taking courses in multivariable calculus, this innovative book aims to make the subject more readily understandable. Differential forms unify and simplify the subject of multivariable calculus, and students who learn the subject as it is presented in this book should come away with a better conceptual understanding of it than those who learn using conventional methods. * Treats vector calculus using differential forms * Presents a very concrete introduction to differential forms * Develops Stokess theorem in an easily understandable way * Gives well-supported, carefully stated, and thoroughly explained definitions and theorems. * Provides glimpses of further topics to entice the interested student

Electricity and Magnetism for Mathematicians

Author: Thomas A. Garrity

Publisher: Cambridge University Press

Published: 2015-01-19

Total Pages: 297

ISBN-13: 1107435161

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Maxwell's equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders.

Book Synopsis Electricity and Magnetism for Mathematicians by : Thomas A. Garrity

Download or read book Electricity and Magnetism for Mathematicians written by Thomas A. Garrity and published by Cambridge University Press. This book was released on 2015-01-19 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maxwell's equations have led to many important mathematical discoveries. This text introduces mathematics students to some of their wonders.

Teaching Electromagnetics

Author: Krishnasamy T. Selvan

Publisher: CRC Press

Published: 2021-06-18

Total Pages: 258

ISBN-13: 1000400581

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Teaching Electromagnetics: Innovative Approaches and Pedagogical Strategies is a guide for educators addressing course content and pedagogical methods primarily at the undergraduate level in electromagnetic theory and its applications. Topics include teaching methods, lab experiences and hands-on learning, and course structures that help teachers respond effectively to trends in learning styles and evolving engineering curricula. The book grapples with issues related to the recent worldwide shift to remote teaching. Each chapter begins with a high-level consideration of the topic, reviews previous work and publications, and gives the reader a broad picture of the topic before delving into details. Chapters include specific guidance for those who want to implement the methods and assessment results and evaluation of the effectiveness of the methods. Respecting the limited time available to the average teacher to try new methods, the chapters focus on why an instructor should adopt the methods proposed in it. Topics include virtual laboratories, computer-assisted learning, and MATLAB® tools. The authors also review flipped classrooms and online teaching methods that support remote teaching and learning. The end result should be an impact on the reader represented by improvements to his or her practical teaching methods and curricular approach to electromagnetics education. The book is intended for electrical engineering professors, students, lab instructors, and practicing engineers with an interest in teaching and learning. In summary, this book: Surveys methods and tools for teaching the foundations of wireless communications and electromagnetic theory Presents practical experience and best practices for topical coverage, course sequencing, and content Covers virtual laboratories, computer-assisted learning, and MATLAB tools Reviews flipped classroom and online teaching methods that support remote teaching and learning Helps instructors in RF systems, field theory, and wireless communications bring their teaching practice up to date Dr. Krishnasamy T. Selvan is Professor in the Department of Electronics & Communication Engineering, SSN College of Engineering, since June 2012. Dr. Karl F. Warnick is Professor in the Department of Electrical and Computer Engineering at BYU.

Book Synopsis Teaching Electromagnetics by : Krishnasamy T. Selvan

Download or read book Teaching Electromagnetics written by Krishnasamy T. Selvan and published by CRC Press. This book was released on 2021-06-18 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Teaching Electromagnetics: Innovative Approaches and Pedagogical Strategies is a guide for educators addressing course content and pedagogical methods primarily at the undergraduate level in electromagnetic theory and its applications. Topics include teaching methods, lab experiences and hands-on learning, and course structures that help teachers respond effectively to trends in learning styles and evolving engineering curricula. The book grapples with issues related to the recent worldwide shift to remote teaching. Each chapter begins with a high-level consideration of the topic, reviews previous work and publications, and gives the reader a broad picture of the topic before delving into details. Chapters include specific guidance for those who want to implement the methods and assessment results and evaluation of the effectiveness of the methods. Respecting the limited time available to the average teacher to try new methods, the chapters focus on why an instructor should adopt the methods proposed in it. Topics include virtual laboratories, computer-assisted learning, and MATLAB® tools. The authors also review flipped classrooms and online teaching methods that support remote teaching and learning. The end result should be an impact on the reader represented by improvements to his or her practical teaching methods and curricular approach to electromagnetics education. The book is intended for electrical engineering professors, students, lab instructors, and practicing engineers with an interest in teaching and learning. In summary, this book: Surveys methods and tools for teaching the foundations of wireless communications and electromagnetic theory Presents practical experience and best practices for topical coverage, course sequencing, and content Covers virtual laboratories, computer-assisted learning, and MATLAB tools Reviews flipped classroom and online teaching methods that support remote teaching and learning Helps instructors in RF systems, field theory, and wireless communications bring their teaching practice up to date Dr. Krishnasamy T. Selvan is Professor in the Department of Electronics & Communication Engineering, SSN College of Engineering, since June 2012. Dr. Karl F. Warnick is Professor in the Department of Electrical and Computer Engineering at BYU.

A Student's Guide to Maxwell's Equations

Author: Daniel Fleisch

Publisher: Cambridge University Press

Published: 2008-01-10

Total Pages: 129

ISBN-13: 1139468472

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Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Book Synopsis A Student's Guide to Maxwell's Equations by : Daniel Fleisch

Download or read book A Student's Guide to Maxwell's Equations written by Daniel Fleisch and published by Cambridge University Press. This book was released on 2008-01-10 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Electromagnetic Fields and Waves in Fractional Dimensional Space

Author: Muhammad Zubair

Publisher: Springer Science & Business Media

Published: 2012-01-03

Total Pages: 82

ISBN-13: 364225358X

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This book presents the concept of fractional dimensional space applied to the use of electromagnetic fields and waves. It provides demonstrates the advantages in studying the behavior of electromagnetic fields and waves in fractal media. The book presents novel fractional space generalization of the differential electromagnetic equations is provided as well as a new form of vector differential operators is formulated in fractional space. Using these modified vector differential operators, the classical Maxwell's electromagnetic equations are worked out. The Laplace's, Poisson's and Helmholtz's equations in fractional space are derived by using modified vector differential operators.

Book Synopsis Electromagnetic Fields and Waves in Fractional Dimensional Space by : Muhammad Zubair

Download or read book Electromagnetic Fields and Waves in Fractional Dimensional Space written by Muhammad Zubair and published by Springer Science & Business Media. This book was released on 2012-01-03 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the concept of fractional dimensional space applied to the use of electromagnetic fields and waves. It provides demonstrates the advantages in studying the behavior of electromagnetic fields and waves in fractal media. The book presents novel fractional space generalization of the differential electromagnetic equations is provided as well as a new form of vector differential operators is formulated in fractional space. Using these modified vector differential operators, the classical Maxwell's electromagnetic equations are worked out. The Laplace's, Poisson's and Helmholtz's equations in fractional space are derived by using modified vector differential operators.

Galileo Unbound

Author: David D. Nolte

Publisher: Oxford University Press

Published: 2018-07-12

Total Pages: 384

ISBN-13: 0192528505

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Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Book Synopsis Galileo Unbound by : David D. Nolte

Download or read book Galileo Unbound written by David D. Nolte and published by Oxford University Press. This book was released on 2018-07-12 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Applied Differential Geometry

Author: William L. Burke

Publisher: Cambridge University Press

Published: 1985-05-31

Total Pages: 440

ISBN-13: 9780521269292

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This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Book Synopsis Applied Differential Geometry by : William L. Burke

Download or read book Applied Differential Geometry written by William L. Burke and published by Cambridge University Press. This book was released on 1985-05-31 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a self-contained introductory textbook on the calculus of differential forms and modern differential geometry. The intended audience is physicists, so the author emphasises applications and geometrical reasoning in order to give results and concepts a precise but intuitive meaning without getting bogged down in analysis. The large number of diagrams helps elucidate the fundamental ideas. Mathematical topics covered include differentiable manifolds, differential forms and twisted forms, the Hodge star operator, exterior differential systems and symplectic geometry. All of the mathematics is motivated and illustrated by useful physical examples.

Electromagnetic Theory and Computation

Author: Paul W. Gross

Publisher: Cambridge University Press

Published: 2011-04-28

Total Pages: 290

ISBN-13: 9780521175234

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Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents. Appendices bridge the gap between the material presented and standard expositions of differential forms, Hodge decompositions, and tools for realizing representatives of homology classes as embedded manifolds.

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

Download or read book Electromagnetic Theory and Computation written by Paul W. Gross and published by Cambridge University Press. This book was released on 2011-04-28 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although topology was recognized by Gauss and Maxwell to play a pivotal role in the formulation of electromagnetic boundary value problems, it is a largely unexploited tool for field computation. The development of algebraic topology since Maxwell provides a framework for linking data structures, algorithms, and computation to topological aspects of three-dimensional electromagnetic boundary value problems. This book attempts to expose the link between Maxwell and a modern approach to algorithms. The first chapters lay out the relevant facts about homology and cohomology, stressing their interpretations in electromagnetism. These topological structures are subsequently tied to variational formulations in electromagnetics, the finite element method, algorithms, and certain aspects of numerical linear algebra. A recurring theme is the formulation of and algorithms for the problem of making branch cuts for computing magnetic scalar potentials and eddy currents. Appendices bridge the gap between the material presented and standard expositions of differential forms, Hodge decompositions, and tools for realizing representatives of homology classes as embedded manifolds.