Matrix Editions current books
5th
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 $87. Sept. 2015
ISBN 9780971576681
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(for books shipped to other countries)
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 PerronFrobenius 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?"
Student
Solution Manual for 5th edition


"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
Look
inside this book (sample pages,
pdf)
Errata
Why a 5th edition?
The
initial impetus for producing a new edition rather than
reprinting the fourth edition was to reconcile differences in numbering
(propositions, examples, etc.) in the first and second printings of the
fourth edition.
An
additional impetus came from discussions John Hubbard had at an
AMS meeting in Washington, DC, in October 2014. Mathematicians and
computer scientists there told him that existing textbooks lack
examples of ``big matrices''. This led to two new examples illustrating
the power of linear algebra and calculus: Example 2.7.12, showing
how Google uses the PerronFrobenius theorem to rank web pages,
and Example 3.8.10, showing how the singular value decomposition
(Theorem 3.8.1) can be used for computer face recognition.
The more we worked on the new edition, the more we wanted to change. An
inclusive list is impossible; here are some additional highlights.
 In
several places in the fourth edition (for instance, the proof of
Proposition 6.4.8 on orientationpreserving parametrizations) we noted
that ``in Chapter 3 we failed to define the differentiability of
functions defined on manifolds, and now we pay the price''.
For this edition we ``paid the price'' (Proposition and Definition
3.2.9) and the effort paid off handsomely, allowing us to shorten
and simplify a number of proofs.
 We rewrote the discussion of multiindex notation in Section 3.3.
 We rewrote the proof of Stokes's theorem and moved most of it out of the Appendix and into the main text.
 We added Example 2.4.17 on Fourier series.
 We rewrote the discussion of classifying constrained critical points.
 We
use differentiation under the integral sign to compute the
Fourier transform of the Gaussian, and discuss its relation to the
Heisenberg uncertainty principle.
 We added a new proposition (2.4.18) about orthonormal bases.
 We greatly expanded the discussion of orthogonal matrices.
 We
added a new section in Chapter 3 on finite probability, showing the
connection between probability and geometry. The new section also
includes the statement and proof of the singular value
decomposition.
 We added about 40 new exercises.
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 5th edition
Math programs
used in the book
Table
of contents (in pdf)
When errata are found, they will be posted at errata

