Even though we do not oficially adopt any textbook for Honors Calc III,
you may find it convenient to get a textbook. Here are some basic hints
to guide your choice:

All calculus textbooks at this level are more or less obese, more or less 
overpriced, more or less cloned from each other, and more or less uninspiring.

You will identify class material by subject names and can find matching stuff
in most textbooks. You may want to get used older editions for a cheaper price,
but restricted availability prevents me from adopting one particular older 
edition of one particular book. I assign my own hwk, so we do not need
textbook uniformity for hwk purposes. 

The following books have been used at UT for 247 in the past:
-- Varberg, Purcell, Rigden (goes for 147-148-247)
-- Hurley: Multi-variable Calculus (this one is out of print with very 
   restricted availability.)

The following is a classic, which will certainly work:
-- Marsden, Tromba: Vector Calculus

We are using 
-- Stewart Calculus (Concepts and Contexts) 
for our non-honors sequence, and I see no reason against using it for 
Honors as well. Only be aware that for maybe one week of class, when we 
are doing `total derivative', the depth of 
Stewart will fall short of the course. 

Among these, Marsden-Tromba is probably closest to the course, with 
Varberg-Purcell-Rigden a close follower. 
Hurley is somewhat similar to the Calc-3 part of Varberg-Purcell-Rigden,
but I am quite unhappy with the geometry-defying introduction of the 
gradient in this book.


There is one more book you might consider to choose, but I need to be very 
specific which expectations it will and will not satisfy: It is 
-- John H. Hubbard, Barbara Burke Hubbard: Vector Calculus, Linear Algebra
   and Differential forms. The 2d edition is from Prentice Hall,
   the 3rd edition from matrixeditions.com
30%  of the book fit maybe 2/3 of Math 247, another 30% could be a good fit 
for an Honors linear algebra course like our 257, and the rest goes beyond
these courses. The authors cater for an approach which would integrate our
247 and 257 into a 2-semester sequence. If you expect a textbook that serves
its purpose during a course and then goes out for resale, then you should NOT
consider this book. If you like a book for keeps to which you will return for 
more details and connections with more advanced material during the rest 
of your UG years, and if you are also taking or will be taking 251 or 257, 
then you should consider the book. It's a real gem. However there will 
be parts of the lecture (multivariable integrals) which the book doesn't 
cater for, because it covers this material at more advanced level than the 
247 course. If you can rely primarily on the lecture, then this should not 
be a big drawback. (I will likely throw in *some* xeroxed material of my own
in this part of the course anyways.)

Be aware that there is a merit in studying MV calculus and linear algebra 
together as a unity. The setup of our curriculum (and of many universities)
does not support this unity. If you have a reference to which to return
while and after studying these two courses, you can regain this unity and 
be so much better prepared for grad studies or 400 level courses. That's 
what I recommend the Hubbard^2 book for. If you need a book that duplicates 
the lecture and would rather not rely on the lecture alone, then Hubbard^2 
would not work so well for you.