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Title: Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach (2nd Edition) by John H. Hubbard, Barbara Burke Hubbard ISBN: 0-13-041408-5 Publisher: Prentice Hall Pub. Date: 15 September, 2001 Format: Hardcover Volumes: 1 List Price(USD): $105.33

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Average Customer Rating: 3.91 (11 reviews)

Rating: 2
Summary: Original Ideas, but Not Ready For Print
Comment: While tying together calculus, linear algebra, and other concepts is unique and interesting, this book should NOT be in print. There are errors in EVERY chapter, and the errata sheet (which is already long) misses many of them. Even important THEOREMS have mistakes. In my opinion, it is an embarrassment.

Further, the notation is needlessly complex. The man may be brilliant, but he does not have much ability in communicating his ideas. While understandable, it takes more work than necessary for an undergraduate text.

Rating: 5
Summary: 2nd edition much improved
Comment: I've read sections of both the first & second editions and the second has numerous minor changes that make it a much better book. The changes are not major--the content and order are almost identical. However, places where the explanations were unclear or difficult frequently have new diagrams or helpful comments in the margins. A few topics that were too difficult or digressions have been moved to appendices or omitted. It remains a challenging book, intended for honors students, but is now a reasonable alternative to Apostol or a sequel to Spivak.

Rating: 5
Summary: A beautiful book for undergrads and grads alike
Comment: Although I am a graduate student in Mathematics, I found
Hubbard's "undergraduate" text to be extremely helpful.
Hubbard combines an intuitive heuristic approach appropriate
for undergraduates with a thoroughly rigorous set of proofs
appropriate for graduate students. I found his discussion of
differential forms particularly helpful. He provides an
excellent intuitive motivation for the definitions, and then
he follows this with a mathematically sound treatment of the
topic. This is a much nicer approach than one will find in
texts such as Rudin's Principals of Mathematical Analysis.
I highly recommend Hubbard's book to anyone wishing to learn
differential forms.

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