The function f(x) is defined by f(x) = 0 1- |×| for |x|≤ 2 for |x| > 2. Calculate the form of f'(x) and plot graphs of both f(x) and f'(x). Calculate directly the Fourier transforms F[f] and F[f] and confirm that F[f'] = ikF[f]. Now consider the Inverse Fourier Transform of F[f], evaluated at x = L sin² k k2 dk = π. 0, to show (1)
The function f(x) is defined by f(x) = 0 1- |×| for |x|≤ 2 for |x| > 2. Calculate the form of f'(x) and plot graphs of both f(x) and f'(x). Calculate directly the Fourier transforms F[f] and F[f] and confirm that F[f'] = ikF[f]. Now consider the Inverse Fourier Transform of F[f], evaluated at x = L sin² k k2 dk = π. 0, to show (1)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
![The function f(x) is defined by
f(x) =
0
1- |×| for |x|≤ 2
for |x| > 2.
Calculate the form of f'(x) and plot graphs of both f(x) and f'(x).
Calculate directly the Fourier transforms F[f] and F[f] and confirm that
F[f'] = ikF[f].
Now consider the Inverse Fourier Transform of F[f], evaluated at x =
L
sin² k
k2
dk = π.
0, to show
(1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffc05cf68-81ae-4970-8864-261fc4d70f9c%2Ff2f67c36-c7f1-4c6a-b37a-cc027b7d7058%2F18jyav_processed.png&w=3840&q=75)
Transcribed Image Text:The function f(x) is defined by
f(x) =
0
1- |×| for |x|≤ 2
for |x| > 2.
Calculate the form of f'(x) and plot graphs of both f(x) and f'(x).
Calculate directly the Fourier transforms F[f] and F[f] and confirm that
F[f'] = ikF[f].
Now consider the Inverse Fourier Transform of F[f], evaluated at x =
L
sin² k
k2
dk = π.
0, to show
(1)
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