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)
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.CR: Chapter 4 Review
Problem 2CR: Determine whether each of the following statements is true or false, and explain why. The derivative...
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