Math 421
See syllabus .
Fall 2004 ( Ed Bueler )

Assignment #11

Due Monday 12/6

From text (Farlow, Partial Differential Equations for Scientists and Engineers):

Lesson 11:  #  1, 2, 3c, 4, 5
Lesson 12:  #  1, 2, 3, 4
Exercise I:  Let f(x) be the function which is periodic on the real line with period  2 pi  and which equals   x   on the interval [0,pi] and equals   - x   on the interval  [-pi,0].  Find the Fourier series of f(x).  Compute the spectrum  c_n = sqrt{ a_n^2 + b_n^2 } and graph it.  Now differentiate the Fourier series term-by-term.  Is the resulting Fourier series the Fourier series of   f ' (x)  ?    Address convergence (using Dirichlet's theorem).

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