Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach

by John H. Hubbard, Barbara Burke Hubbard

Fifth edition of a combined vector calculus, linear algebra, and differential forms textbook, including new material such as "an example showing how Google uses the Perron-Frobenius theorem to rank web pages, and an example showing how the singular value decomposition can be used for computer face recognition." Student solution manual also available (ISBN 978-0-9715766-9-8).

Genres: Mathematics, Textbooks, Science, Calculus, Physics, Academic, Nonfiction

818 pages, Hardcover

First published January 1, 1998

Reviews

[Ronald Lett · Rating 5 out of 5]

An excellent companion to Spivak's "Calculus on Manifolds", this text engagingly bridges the gap between the Gibbs formulation of vector calculus and the modern Cartan formulation using differential forms so that one can properly study differential geometry. Gives many excellent exercises and examples of curious behavior. It is also exceptionally reader-friendly; the authors sprinkle historical anecdotes and modern applications throughout the text and have a voice that is very down-to-earth.

[Parsa · Rating 5 out of 5]

I read parts of the last chapter to help me with Spivak and it was really really good. It does in 150 pages what spivak does in about 40, which is mostly a testament of how terse the latter is. I expect to return to this this term for my diff geo class.

[Matt Tokunaga · Rating 5 out of 5]

A classic for a reason. A bit difficult as an introduction to multivariate calculus and proofs though. Goes off the rails a bit when differential forms are introduced but the payoff is worth it. Once you get to generalized Stokes theorem its very satisfying in its simplicity, though its only simple because of all the knowledge you build up beforehand.

[Daniel Zelich · Rating 3 out of 5]

Introduced me to higher math but this book is terribly written. Pedagogically dubious (manifolds after a chapter of multi and lin alg is not conducive to good understanding) and too numerical in its proofs, but otherwise interesting and fun to read.

[Himanshu Singla]

Its good for which class and is it best for 12th standard