M 412 Fall 2007
HOMEWORK SUMMARY REPORT
Chapter number: 12
Section number: 2
Exercise number: 2,3
Number of papers received: 10
Reviewing committee: alpha
List all participating committee members:
Travis Trahan, Gary Chen
Author(s) of paper(s) chosen for publication: Michael Naramore
Comments: every student for the correct answer on 12.2.2; however, for
12.2.3, the majority of people for an incorrect answer, and most of people
who have the wrong answer made the same mistake by skipped a few crucial
steps when applying the condition w(0,t)=sin(3t) in problem 12.2.3. The
reason we chose Naramore's paper is beacuse his answer was correct,
concise and included all the necessary steps. There are total of 17 papers
we have received to review, but only 10 people had included their email
address in their paper. So we did review all 17 papers but were only be
able to submit 10 papers that included their email address.The people who
did not included their email address are ...
GRADER'S COMMENT: Here is a method for 12.2.3:
Let z(s) = w(x+4s, t+s).
dz/ds = 4Dw(x+4s, t+s) + w't(x+4s, t+s) = 0.
So 0 = z(0) - z(-x/4) = w(x,t) - w(0,t- x/4) = w(x,t) = sin[3(t- x/4)].
Thus, w(x,t) = sin(3t - 3x/4).