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Consider the function if -a < x < 0 f(x) = if x = 0 if 0

Consider the function if -a < x < 0 f(x) = if x = 0 if 0

Advanced Engineering Mathematics
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.
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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