Matrix Editions current books
4th
edition
Vector
Calculus, Linear Algebra, and Differential
Forms: A Unified Approach
John
Hubbard and Barbara Burke Hubbard


818
pages, hardcover, smythesewn binding, 8 x 10 inches $84. Sept. 2009
ISBN 9780971576650
"Superb
on all counts"  review in CHOICE (review of 1st
edition)
"A real
gem"  review of 2nd edition, MAA Monthly
Praise from readers
Reprinting of 4th edition
The
4th edition now exists in two printings. To determine which printing you have, look at the copyright page.
If the numbers under ``Printed in the United States of America''
decrease from 10 to 1, it is the first printing. If they decrease
from 10 to 2, it is the second printing. The second printing corrects
all errata known at time of printing.
When we ran low on copies of the first printing, we chose not to make it a new edition, so that students can use both printings in a single classroom. The result is that there are
some discrepancies in numbering, particularly in Sections 4.3 and
4.4. Correspondences between the two printings are described in the table of correspondences, which is in pdf.
Why a 4th edition?
The
main impetus was that we finally hit on what we consider
the right way to define orientation of manifolds. The new approach,
based on direct bases, is
simpler than
the previous, but still covers the case of 0dimensional manifolds
(i.e., points). In addition, the new edition provides
 a proof of Gauss's remarkable
theorem.
This theorem, also known as the ``Theorema
Egregium'', justifies the
statement (section 3.8) that Gaussian curvature measures to
what
extent pieces of a surface can be made flat, without stretching or
deformation. All the other proofs we know of this theorem
require
advanced techniques; the proof we added to section
5.4 uses only the
techniques developed in this book.
 a
justification of the statement in section 3.8 that the mean
curvature measures how far a surface is from being
minimal
 classifying constrained
critical points using the augmented
Hessian matrix (section 3.7)
 a proof of Poincare's lemma
for arbitrary forms rather than just 1forms, based on the cone operator
(section 6.12)
 a discussion of Faraday's
experiments in section 6.11 on electromagnetism
 a trick for finding Lipschitz
ratios for polynomial functions (example 2.8.12)
We
have also added new examples and exercises, deleted some weaker
examples and exercises, and corrected errata.
Preface
(excerpt in html, with link to complete preface in pdf)
To order (for
books
shipped to the United States)
To
order
(for books shipped to other countries)
Student
Solution Manual for 4th edition
Math programs
used in the book
Table
of contents (in html)
Look
inside this book (sample pages,
mostly in pdf)
For errata listings, go to errata

