M 412 Fall 2007
HOMEWORK SUMMARY REPORT
Chapter number: 7
Section number: 10
Exercise number: 12
Number of papers received: 3
Reviewing committee: Gamma
List all participating committee members:
Michael Naramore, Nick Boehmisch
Author(s) of paper(s) chosen for publication: [Angela Sung]
Comments:
The main problem that was made was that some people made an
assumption of symmetry at the beginning of the problem; they said
that the problem was independent of theta (which it is not). This was a
difficult problem to grade as well, because there is no
previous solution on the web. I submit Angela Sung's report to be
published
since hers is the most correct (as far as we can tell).
INSTRUCTOR'S COMMENT: As discussed in class, the best symmetry to impose
is that the data function is symmetric under reflection through the
equator. Angela tried a different symmetry, which would be equally valid
(since the data on the bottom half of the sphere can be chosen as whatever
is convenient), but she ran into some trouble implementing it. The key
fact to use is that P_l^m(z) is an even function if l+m is even and an odd
function if l+m is odd; only the odd cases can occur in this problem.