M 412 Fall 2006
HOMEWORK SUMMARY REPORT
Chapter number: 3
Section number: 2
Exercise number: 2
Number of papers received: 7
Reviewing committee: Zeta
List all participating committee members:
James Burger, Dakota Blair
Author(s) of paper(s) chosen for publication:
Stacy Lodden
Comments:
Overall the results were correct with a few mistakes involving the
sketches and final answers to part (b). The most common mistake was to
sketch the series incorrectly. Although many correctly showed the
periodicity, few indicated the values of the series at the jump
discontinuities. One paper also sketched a partial sum of the Fourier
series instead of the series itself. The paper chosen for publication
correctly sketched this in a very clean manner. Of the papers which had
correct answers on part (b), they almost invariably did not collect the
terms for $b_n$ and $a_n$ for $n>0$ to reveal a factor of $\sinh L$.
Generally the papers which got this part wrong had attempted to collect
the $\sinh L$ terms, but instead of $L$ wrote other (understandable but
incorrect) arguments, such as $n \pi$. Most also did not convert $\cos (n
\pi)$ into $(-1)^n$, including the paper chosen for publication. There are
a few reasons why this step towards creates a better answer, but its
exclusion does not make the conclusion incorrect. The reasons for
replacing $\cos (n \pi)$ with $(-1)^n$ include the fact that it is shorter
to speak, write and type, but perhaps the most important reason one should
consider doing this is in numerical computation. A program which is not
using symbolic computation would have to use an approximation for $\pi$
which would get worse as $n$ became large, however the exact calculation
of $(-1)^n$ is independent of however large the chosen $n$. Almost all
papers correctly calculated the coefficients for part (f).
The recommendation of the reviewing team is that Stacy Lodden's paper be
converted into \LaTeX\, implementing our suggestions and published as a
solution to this problem.