PHGN311 Homework #6
Due Friday, Oct. 11, 2013 at the beginning of class
Finish Chapter 7 on Fourier Series and Transforms. Show your work on all problems.
Use Mathematica to check results but not as a solution itself unless asked to.
1. Boas 7.5.11 (include a plot of the function along with a sum of the series through the
2nd and 10th harmonics. Plot from -2π to 2π).
2. Boas 7.6.3 (explain your answer).
3. Boas 7.6.14
4. Boas 7.7.11
5. Boas 7.8.14
6. Using Mathematica, or equivalent code, sketch the following functions and obtain the Fourier trig series (assuming 2π periodicity) for each (I don’t expect you to solve these by hand, its ok to just rely on the symbolic manipulation as long as it gives good answers you believe.)
a) f(x) = x for -­‐π < x < π b) f(x) = -­‐x for -­‐π < x < 0 and f(x) = x for 0 < x < π c) f(x) = 0 for -­‐π < x < 0 and f(x) = x for 0 < x < π Now plot all three Fourier series for the sum of, quite a few terms, enough to make a good approximation to the function, in the region -­‐π < x <π. Discuss the similarities in your answers in the region 0 < x < π in terms of concepts like Fourier sine series, Fourier cosine series, and different ways we can represent the same function. Does any choice appear to be better than the others for representing the region 0 < x <π? Can you speculate way?