Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to McCallum's book, the required text for the course. You should write up solutions neatly to all problems, making sure to SHOW ALL YOUR WORK. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be your own work.

**Section 14.1**

Problems: 2, 3, 8, 11, 14, 15, 18

*Hint:* For problem #8, try subtracting the equations f_x = 0 and
f_y = 0, to find a relation between x and y. Then plug back into f_x = 0
and solve.

**Section 14.2**

Problems: 2, 3, 14

*Note:* Since there are two problems on the computer project (least squares and celestial
mechanics) which involve applications of min-max problems, I have assigned fewer problems
from Section 14.2.

**Section 14.3**

Problem: 2, 3, 8, 12, 15

*Note:* For problems #12 and #15, search for critical points in both the interior of the
region and on the boundary. The boundary of the region is the constraint for using
the method of Lagrange Multipliers.