) If F(ƒ) = ƒ(§) is the Fourier transform of f(x), show that the Fourier transform of x f(x) is F(xf) = ¸df dε' where is the Fourier transform variable. O Airy's equation is d²u xu = 0. dx² Use Fourier transforms and the result of part (a) to show that, by a suitable choice of a constant of integration, Airy's equation has the Airy function solution 1 Ai(x)= ½ cos (}§³+x) d£. π = COS

) If F(ƒ) = ƒ(§) is the Fourier transform of f(x), show that the Fourier transform of x f(x) is F(xf) = ¸df dε' where is the Fourier transform variable. O Airy's equation is d²u xu = 0. dx² Use Fourier transforms and the result of part (a) to show that, by a suitable choice of a constant of integration, Airy's equation has the Airy function solution 1 Ai(x)= ½ cos (}§³+x) d£. π = COS

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

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