PHGN311 Homework #5
Due Friday, Sep. 27, 2012 at the beginning of class
Finish Chapter 4 on partial derivatives and begin reading Chapter 7 on Fourier Series.
Show your work on all problems. Use Mathematica to check results but not as a solution
itself unless asked to. Fourier Series are such an important topic that I will include a
Fourier Series question on the upcoming test. So you need to practice being able to
simplify the problem, identify symmetries and terms that won’t be present, and finding
the series. Try treating the Fourier Series questions, initially, as if they are test questions.
Challenge yourself to get started and find the solution without going to your textbook.
Likely you will have to at first, but as you practice this a bit more, it should become more
familiar and your need for your book or notes will be much less.
1. Boas 4.6.7 (the plotting on this one can be confusing since roots of the equation can
give complex numbers. Mathematica, however, has the nice habit of only plotting
real numbers even if you put in an expression that for some values is complex).
2. Boas 4.7.15
3. Boas 4.11.1
4. Boas 4.12.12 (don’t forget to take into account that the variable x is in the limits and
in the integrand!)
5. Boas 7.4.13
6. Boas 7.5.1 (This is an easy one because it’s very similar to the text and class example.
This give you the chance to think about it, see if you guess the answer just by a shift
of coordinates or a change of sign. Include a plot of f(x), the sum of the series
through the 2nd harmonic, and the sum of the series through the tenth harmonic. Plot
from -2π to 2π.)
7. Boas 7.5.6 (sketch this one first. Think about whether you could get the answer from
the square wave solution worked out in the text without doing all the work? But then
go ahead and formally find the Fourier Series. Again, include a plot of f(x), the sum
of the series through the 2nd harmonic, and the sum of the series through the tenth
harmonic. Plot from -2π to 2π.)
8. Boas 7.5.10 (include a plot of f(x), the sum of the series through the 2nd harmonic,
and the sum of the series through the tenth harmonic. Plot from -2π to 2π.)