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Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Us Mathematica or another tool to do this.)

Let f be the function defined for - ≤ x ≤ π by 1 0 f(x) if - π/2 ≤ x ≤ π/2 otherwise and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Us Mathematica or another tool to do this.)

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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Let f be the function defined for -≤ x ≤ π by 1 f(x) = 0 and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Use Mathematica or another tool to do this.) Here is the plot of this function; it's a square wave. -3 -2 -1 0.8 0.6 0.4 0.2 if π/2 ≤ x ≤ π/2 otherwise 2 3
Transcribed Image Text:Let f be the function defined for -≤ x ≤ π by 1 f(x) = 0 and then extended to be 27-periodic on the real number line. Part (a): Find the Fourier cosine series for this function. Part (b): Plot the first five terms of the series to see how well it approximates the function. (Use Mathematica or another tool to do this.) Here is the plot of this function; it's a square wave. -3 -2 -1 0.8 0.6 0.4 0.2 if π/2 ≤ x ≤ π/2 otherwise 2 3
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