|
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, smythe-sewn binding, 8 x 10 inches $79. Sept. 2009
ISBN 9780971576650
"Superb
on all counts" - review in CHOICE (review of 1st
edition)
"A real
gem" - review of 2nd edition, MAA Monthly
More
reviews and reader praise for first three editions
Why a
new 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 0-dimensional 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 1-forms, 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)
|
|