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

5th edition

John H. Hubbard and Barbara Burke Hubbard

ISBN 9780971576681

818 pages, Hardcover, smythe-sewn binding
8 x 10 inches, 2015, $110

A pdf version is available. Please read this before ordering.

pdf ebook, $87

Both print and pdf ebook, $149

The Student Solution Manual for this textbook is 305 pages, soft cover, 8x 10 inches.

Print book, $38

pdf ebook, $33

Both print and pdf ebook, $55

Please consider recommending that your university or department librarian order this book. Thank you!

For more information, click on the links below.

Why a 5th edition?
Sample pages
Superb on all counts — review in CHOICE (review of 1st edition)
A real gem — review of 2nd edition, MAA Monthly
Praise from readers
Review of 3rd edition, MAA Reviews
Errata

Correspondences between the first and second printings (This concerns numbering in Section 2.6.)

This 5th edition contains all the things that made the earlier editions different from other textbooks. Among others:

• Integrating linear algebra and multivariable calculus


• Using effective algorithms to prove the main theorems (Newton's method and the implicit function theorem, for instance)


• A new approach to both Riemann integration and Lebesgue integration


• Manifolds and a serious introduction to differential geometry


• A new way of introducing differential forms and the exterior derivative.

There is also new material, in response to requests from computer science colleagues:

• More big matrices! We included the Perron-Frobenius theorem, and its application to Google's PageRank algorithm


• More singular values! We included a detailed proof of the singular value decomposition, and show how it applies to facial recognition: "how does Facebook apply names to pictures?"