An introduction to multivectors, dyadics, and differential forms
for electrical engineers
"The author is a true scholar with an unusual sense of time,
place, and history. He is internationally well known and respected.
His knowledge of differential forms is equaled by only a tiny
number of electromagnetic researchers, most of whom were associated
with Professor Deschamps, either as colleagues or students. The
presentation in this book is a true reflection of the author's
grasp of the subject and his skills as a writer."
-Professor Donald G. Dudley, Editor, IEEE Press Series on
Electromagnetic Wave Theory
"Professor Deschamps' goal of completing a monograph on
differential forms and their applications to electromagnetics was
never realized. I, like most of his students, fondly remember the
excitement and challenges that his interest in differential forms
brought to our lives. With the kind dedication of his book to
Professor Deschamps and his expert presentation of this very
mathematically challenging representation of electromagnetic
phenomena, Professor Lindell nicely conveys those feelings to the
reader."
-Professor Richard W. Ziolkowski, University of Arizona
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
themathematical 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.
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