There is now a 4th edition of this book
Vector
Calculus 4th edition
3rd edition
ISBN
9780971576636
802 pages, hardcover,
smythesewn binding, $78, June 2007
Course adoptions at
Cal State East Bay, Cornell University, Harvard University, the
HarvardWestlake School,the Hotchkiss School, Indiana University, Indiana
UniversityPurdue University Indianapolis, UC San Diego, the University
of Minnesota, the University of Montana, the University of Chicago
Laboratory Schools, the University of South Dakota, Washington
University in St. Louis, the Wheeler School
MAA Review: "When
reading this book, I
constantly was aware of the fact that I would have
benefited immensely if I had gotten my hands on it when I was an
undergraduate... I
was very
impressed with the depth, clarity and ambition of this book.
It respects its readers, it assumes that they are intelligent and
naturally curious about beautiful mathematics. Then it provides them
with all the tools necessary to learn multivariable calculus, linear
algebra and basic analysis." — Gizem
Karaali, assistant professor of Mathematics at Pomona College Read entire review
Praise from readers:
"I've
begun reading the book and have quickly come to truly love its
approach. As a high school calculus teacher, I've read many a
linear algebra text and many multivariate calculus books as well.
A former student of mine, currently an undergraduate ... at Harvard,
recommended yours... and it has lived up to all the praise he has
heaped upon it.
I truly value the approach you take to try to foster true understanding
(including the amazingly helpful margin notes that dot each chapter),
the obvious deep thought you put into the order in which all the
material is presented, and the clear desire it seems the authors have
to truly share their expertise in the subject in a way most likely for
the target audience to fully benefit from it." — Ross Lipsky
Valley Stream South High School Mathematics Department
"Thank you for this gold mine! (and for the cheap price too, especially for European people!)" — Marc Chambon, graduate student in inorganic chemistry and chemical engineering, Université Via Domitia, Perpignan, France
"I
am having a great time reading the third edition of your book (and
attempting all the problems). It's quite user friendly without
being sappy... I particularly enjoyed problem A1.5  I thought I'd
never see how Peano did it. Part c. is worth the answer
book alone." —Lewis Robinson, retired M. D. indulging a lifelong taste for mathematics
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 3rd edition
Math programs used in the book
Table
of contents (in html)
Look
inside this book (sample pages, mostly in pdf)
Errata (latest posting March 23, 2008)
Readers
praise first two editions
"Superb
on all counts"  review in CHOICE (review of 1st
edition)
"A real gem"  review of 2nd edition, MAA Monthly
3 new
sections:
 Eigenvectors and eigenvalues Section 2.7 on eigenvectors, eigenvalues, and
diagonalization bypasses
the determinant; a few pages in chapter 4 connect this discussion with
determinants and the characteristic
function.
 Integration and
curvature Section 5.4
discusses the Gauss map.
 Electromagnetism and
differential forms (Section 6.9)
Other
changes compared to the 2nd edition:
 New examples
Notably an extended example on checking boundary points when looking
for critical points of functions
 Uniqueness of row echelon
form The first and second
editions left the proof of uniqueness in theorem 2.1.8 as an exercise.
Now this important result is in the text.
 New exercises Including
an exercise proving a version of Kantorovich's theorem with a weaker
continuity condition on the derivatives; this has implications for the
inverse and implicit function theorems.
 New proof of the generalized
Stokes's theorem
 Programs posted on web No
more laborious typing! The three programs used in the book
are available for cutandpaste at math programs.

