Reference no: EM131103939
Math 054 Partial Differential Equations - HW Assignment 9
1. Is it possible to find two functions in L2(-∞, ∞) neither one of which is identically zero but whose convolution product is zero?
2. Consider a function f(x) in L2(-∞, ∞) with Fourier transform F(α) and let
g(x) = F-1[F(α)IA(α)], for some A > 0
In what way, if any, is g(x) related to f(x).
3. Solve the following by taking the Fourier Transform with respect to x.
ut = c2uxx, t > 0
u(x, 0) = f(x), -∞ < x < ∞
4. Let k denote a positive integer and let
Compute the Fourier transform Fk(α) for k = 1, 2, ... and sketch the graphs of fk(x) and Fk(α) for k = 1, 2, 3. Relate the changes in fk(x) as k varies to the corresponding changes in Fk(α).
5. Solve the following by taking the Fourier Transform with respect to x.
utt(x, t) = a2uxx, t > 0
u(x, 0) = 0, ut(x, 0) = sin πx, -∞ < x < ∞
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: Math 054 Partial Differential Equations - HW Assignment 9. Compute the Fourier transform Fk(α) for k = 1, 2, ... and sketch the graphs of fk(x) and Fk(α) for k = 1, 2, 3. Relate the changes in fk(x) as k varies to the corresponding changes in Fk(α)
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