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Rating: 
Summary: A good introduction to forms
Review: Fortunately there are several books, at an introductory level suitable for undergraduate students, on how differential forms constitute a "new" powerful mathematical technique that surpasses the outdated vector calculus. This book by Steven H. Weintraub is a very good example among others -- such as: (i) "Advanced Calculus: A Differential Forms Approach" by Harold M. Edwards (Birkhäuser, Boston, 1994); (ii) "Vector Calculus, Linear Algebra, and Differential Forms" by John H. Hubbard and Barbara Burke Hubbard (Prentice Hall, NJ, 2nd ed., 2002).
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. However, this book shows that it is possible to make an introduction to forms without mastering such concepts in topological and smooth manifolds -- although there is an extensive bibliography on this subject out there (the books by John M. Lee on manifolds are my favorite).
For more advanced readers, the book by Friedrich H. Hehl and Yuri N. Obukhov on the "Foundations of Classical Electrodynamics" (Birkhäuser, Boston, 2003) is, in my opinion, the most elegant exposition on the relation between electromagnetism and forms.
Rating: 
Summary: VERY CLEAR BOOK ON DIFFERENTIAL FORMS
Review: I recommend this book to anyone who wants a quick introduction to differential forms without getting lost in a sea of mathematical formalism. The author explains the ideas very well. The exercises in the book are fairly easy to solve. I haven't noticed any misprints so far as the other reviewer claims but should there by any I am sure they can be corrected with intuition alone. This is a very intuitive book that can serve as a companion text to the authoritative book on "DIFFERENTIAL FORMS" by Edwards which I have also reviewed.
Rating:
Summary: VERY CLEAR BOOK ON DIFFERENTIAL FORMS
Review: I recommend this book to anyone who wants a quick introduction to differential forms without getting lost in a sea of mathematical formalism. The author explains the ideas very well. The exercises in the book are fairly easy to solve. I haven't noticed any misprints so far as the other reviewer claims but should there by any I am sure they can be corrected with intuition alone. This is a very intuitive book that can serve as a companion text to the authoritative book on "DIFFERENTIAL FORMS" by Edwards which I have also reviewed.
Rating:
Summary: good introduction
Review: The language of differential forms presented at the level of this student-friendly text provides a refreshing outlook on vector analysis. And with a view towards more advanced courses, this book hints at the remarkable computational prowess it bears on differential geometry at large.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. Have fun!
Rating: 
Summary: Very confusing....
Review: 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.
Rating:
Summary: Very confusing....
Review: 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.
Rating:
Summary: Intuitive Book
Review: This is the only book on the subject I know of that gives me a feel for what is going on. To many other books are long on notation and short on insight. Occasionally the book seems to plod but that is a minor problem compared with the dense presentation of other books. Highly recommended.
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