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Differential Forms: A Complement to Vector Calculus 1st Edition
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Top Customer Reviews
As far as I know, it was in "Gravitation" -- by Charles W. Misner, Kip S. Thorne and John Archibald Wheeler (Freeman, San Francisco, 1973) -- that a pictorial representation of forms was clearly presented to physicists for the first time. These authors went even further, explaining how "forms illuminate electromagnetism, and electromagnetism illuminates forms" (p. 105).
However, until now, it seems that in engineering forms have been disregarded -- despite early attempts by George A. Deschamps (see, e.g., his paper "Electromagnetism and differential forms", Proc. IEEE, Vol. 69, pp. 676-679, 1981), not to mention Harley Flanders's book ("Differential Forms with Applications to the Physical Sciences", Dover, NY, 1989). Perhaps the book by Ismo V. Lindell ("Differential Forms in Electromagnetics", IEEE Press/Wiley, NJ, 2004) will be able to change this sad scenario.
It seems that the difficulty lies mainly in the fact that a proper understanding of k-forms, as antisymmetric (0,k) tensors in differentiable manifolds, requires the study of technical demanding subjects such as de Rham cohomology.Read more ›
In light of the author's heuristic approach, the book does well in setting the stage for the applications he has in mind (casting Stokes' theorem in its true form, for example).
One should then go on to read books like Do Carmo, written in a similar vein, but this time, delineating the algebraic machinery needed to set up the theory in a more rigourous framework.
Most Recent Customer Reviews
I don't see what the hype is about differential forms. They are just antisymmetric tensors. Big deal. Read morePublished on September 6, 2008 by LB
This book was a very confusing book on a very confusing topic. I am looking forward to the day that someone can write an understandable treatise on this subject.Published on June 22, 2004 by mathman