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).
Office: Chapman 301C. 474-7693
ffelb@uaf.edu
www.math.uaf.edu/~bueler/