Consider the function if -a < x < 0 f(x) = if x = 0 if 0
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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alpha=1
beta=6
gamma=13
![10 4.
Consider the funcțion
if -a <a <0
if x = 0
f(x) =
if 0 <x <a
(a) Plot the Nth partial sum the Fourier sine series of f(æ) for N = 5, 10, 50, and 200
along with ƒ (x) for -a < ¤ < a.
(b) Show that each of the maximum overshoots occurs near a discontinuity and that
they approach a limit which is approximately 9% more than the magnitude of the
jump at the discontinuity. This behavior is the Gibbs Phenomenon that was
mentioned in the class.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F57d168b8-181c-4cdd-98db-4d6895d93f9d%2F11cab9aa-e2ca-452f-9ffc-ddfbac016f86%2Fybl20j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:10 4.
Consider the funcțion
if -a <a <0
if x = 0
f(x) =
if 0 <x <a
(a) Plot the Nth partial sum the Fourier sine series of f(æ) for N = 5, 10, 50, and 200
along with ƒ (x) for -a < ¤ < a.
(b) Show that each of the maximum overshoots occurs near a discontinuity and that
they approach a limit which is approximately 9% more than the magnitude of the
jump at the discontinuity. This behavior is the Gibbs Phenomenon that was
mentioned in the class.
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