MAT331 homework problems
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.
- (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?
- (expires 2/25) With reference to Problem #11, show that, for , the
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 .