Consider a periodic function f(x) with period 2π defined as follows. In the region −π ≤ x ≤ π, define it as f(x) = x , and for all x outside the range −π ≤ x ≤ π define it by the periodicity condition f(x + 2π) = f(x). Sketch a graph of the function then derive expressions for the coefficients a0, ak and bk in the expansion provided
Consider a periodic function f(x) with period 2π defined as follows. In the region −π ≤ x ≤ π, define it as f(x) = x , and for all x outside the range −π ≤ x ≤ π define it by the periodicity condition f(x + 2π) = f(x). Sketch a graph of the function then derive expressions for the coefficients a0, ak and bk in the expansion provided
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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Consider a periodic function f(x) with period 2π defined as follows. In the region −π ≤ x ≤ π, define it as f(x) = x , and for all x outside the range −π ≤ x ≤ π define it by the periodicity condition f(x + 2π) = f(x).
Sketch a graph of the function then derive expressions for the coefficients a0, ak and bk in the expansion provided.
Transcribed Image Text:ao
f (x) =
+> (ãk sin(kax)+ ak cos(kx))
k=1
using the formulae
T
1
- f(2) cos(ka) dæ
- f(x) sin(kæ) dæ
ak
and
- T
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