GRADER'S COMMENTS ON WEEK 12:
There is a dangerous misprint in the textbook. The first equation of Sec.
7.10.5 and equation (7.10.29) clearly should have been written like
equations (7.7.45), (7.8.5), and (7.9.20), just to name a few examples.
More precisely, the sine and cosine functions are ALTERNATIVES, not
factors to be multiplied together! Several students blindly copied these
equations into their solutions to exercises 7.10.1 and 7.10.3.
The reviewers of 7.10.3 say of the formula for the coefficients that "it
is unclear how to come up with that solution." Moroever, most students
have been giving wrong formulas for the coefficients in various series
(not just in that exercise), the main mistakes being forgetting to include
the right weight in the integral or to divide by the appropriate
normalization denominator given by another integral. Memorizing or
guessing the formulas without complete understanding of what's going on
will work when only simple things like sines and cosines are involved, but
now you need to review how in general the coefficients can be obtained via
the orthogonality properties of the families of functions involved.
INSTRUCTOR'S COMMENT ON WEEKS 11 AND "12":
Because the semester was effectively over before the papers were reviewed
and graded, papers marked "revise" will have to be accepted as is. Pay
close attention to "Grader's comments" in the reports.