Matrix Editions current books
Calculus, Linear Algebra, and Differential
Forms: A Unified Approach
Hubbard and Barbara Burke Hubbard
pages, hardcover, smythe-sewn binding, 8 x 10 inches $79. Sept. 2009
on all counts" - review in CHOICE (review of 1st
gem" - review of 2nd edition, MAA Monthly
reviews and reader praise for first three editions
Reprinting of 4th edition
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?
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
the previous, but still covers the case of 0-dimensional manifolds
(i.e., points). In addition, the new edition provides
have also added new examples and exercises, deleted some weaker
examples and exercises, and corrected errata.
- a proof of Gauss's remarkable
This theorem, also known as the ``Theorema
Egregium'', justifies the
statement (section 3.8) that Gaussian curvature measures to
extent pieces of a surface can be made flat, without stretching or
deformation. All the other proofs we know of this theorem
advanced techniques; the proof we added to section
5.4 uses only the
techniques developed in this book.
justification of the statement in section 3.8 that the mean
curvature measures how far a surface is from being
- classifying constrained
critical points using the augmented
Hessian matrix (section 3.7)
- a proof of Poincare's lemma
for arbitrary forms rather than just 1-forms, based on the cone operator
- 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)
(excerpt in html, with link to complete preface in pdf)
To order (for
shipped to the United States)
(for books shipped to other countries)
Solution Manual for 4th edition
used in the book
of contents (in html)
inside this book (sample pages,
mostly in pdf)
For errata listings, go to errata