MAT331 homework problems

**NOTE:**
Neither of these problems involve `Maple`, except as a word processor to
write your solution. If you like, you are welcome to turn in a printed
or handwritten version, if you are more comfortable with that.

**11.**- (
*expires 2/25*) Following Section 4 of the notes, prove that if we describe the circle of center and radius using the parameters , with , rather than the more natural parameters , then the error function is quadratic in and . What does this imply about the number of critical points? **12.**- (
*expires 2/25*) With reference to Problem #11, show that, for , the transformation is a valid change of variables, that is, it is one-to-one. This should help you prove that has only one ``physical'' critical point, which is a minimum, and is mapped, through the transformation, into the unique critical point of .

MAT 331 2002-02-18