Below are some extra practice problems, in no particular order.  I'll update this list periodically.  They're all of medium to hard difficulty.

Make sure you can do basic problems on any topic covered in lecture!  A good guideline for topics covered in lecture is the list of topics on the lecture schedule page.  If you have any questions about whether a particular concept is important, definitely just email me and ask.

Written by me:
If f is an infinitely differentiable function of two variables such that the gradient of f is the zero vector for all x and y, must f be constant?  Why or why not?
One checks that f(x,y)=x^2 +y^2 satisfies f_x = 2x, f_y= 2y. What other infinitely differentiable functions f(x,y) satisfy this?  Find all of them.

From the book:

10.1 43
10.2 73
10.3 70
10.4 31

Chapter 10, Problems Plus: 1, 4, 5 (a-g)

12.1 38
12.2 41
12.3 59
12.4 50
12.5 59
12.6 46

Chapter 12, Problems Plus: 4, 5

13.1 21-24
14.1 61, 63, 64
14.3 77
14.5 54
14.6 56
14.7 29, 56
14.8 42
Chapter 14, Problems Plus: 1, 2, 5, 7, 8