PROJECT. Properties of Fourier Integrals (a) Fourier
Chapter 11, Problem 11.7(choose chapter or problem)
PROJECT. Properties of Fourier Integrals (a) Fourier cosine integral. Show that (11) implies (al) f(ax) = ~ fO A( :) cos xw dw (a2) (a3) (a> 0) (Scale change) xf(x) = fOO B*(w) sin xw dw, o dA B* = - dw ' A as in (10) x 2f(x) = f=A*(W) cosxw dw, o d2 A A* = - dw2 . (b) Solve Prob. 8 by applying (a3) to the result of Prob.7. (c) Verify (a2) for f(x) = I if 0 < x < a and f(x) = 0 if x > a. (d) Fourier sine integral Find formulas for the Fourier sine integral similar to those in (a).
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