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Differential Forms: A Complement to Vector Calculus 1st Edition

3.4 out of 5 stars 7 customer reviews
ISBN-13: 978-0127425108
ISBN-10: 0127425101
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Editorial Reviews

About the Author

Steven H. Weintraub is a Professor of Mathematics at Lehigh University. He received his Ph.D. from Princeton University, spent many years at Louisiana State University, and has been at Lehigh since 2001. He has visited UCLA, Rutgers, Oxford, Yale, Gottingen, Bayreuth, and Hannover. Professor Weintraub is a member of the American Mathematical Society and currently serves as an Associate Secretary of the AMS. He has written more than 50 research papers on a wide variety of mathematical subjects, and ten other books.
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Product Details

  • Hardcover: 268 pages
  • Publisher: Academic Press; 1 edition (August 20, 1997)
  • Language: English
  • ISBN-10: 0127425101
  • ISBN-13: 978-0127425108
  • Product Dimensions: 6 x 0.6 x 9 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 3.4 out of 5 stars  See all reviews (7 customer reviews)
  • Amazon Best Sellers Rank: #1,939,740 in Books (See Top 100 in Books)

Customer Reviews

Top Customer Reviews

By Prof C. R. PAIVA on August 14, 2004
Format: Hardcover
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undergraduate students, on how differential forms constitute a "new" powerful mathematical technique that surpasses the outdated vector calculus.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.
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Format: Hardcover
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.
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Format: Hardcover
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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Format: Hardcover
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!
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