(b) (c) (d) (e) (f) Consider the function f(x) = |x| over the interval – L≤ x ≤ L. Derive the Fourier sine series over the interval −L ≤ x ≤ L. = = L Derive the Fourier cosine series over the interval –L ≤ x ≤ L. Derive the full periodic series over the interval -L ≤ x ≤ L. For each series computed in parts (a) - (c) what is the value at x Which of the series in parts (a) - (c) can be differentiated term by term so that the resulting series converges to the derivative of f(x) with respect to x over the interval -L≤ x ≤ L? Which of the series in parts (a) - (c) can be integrated term by term so that the resulting expression converges to the integral S* f ( x') dx'
(b) (c) (d) (e) (f) Consider the function f(x) = |x| over the interval – L≤ x ≤ L. Derive the Fourier sine series over the interval −L ≤ x ≤ L. = = L Derive the Fourier cosine series over the interval –L ≤ x ≤ L. Derive the full periodic series over the interval -L ≤ x ≤ L. For each series computed in parts (a) - (c) what is the value at x Which of the series in parts (a) - (c) can be differentiated term by term so that the resulting series converges to the derivative of f(x) with respect to x over the interval -L≤ x ≤ L? Which of the series in parts (a) - (c) can be integrated term by term so that the resulting expression converges to the integral S* f ( x') dx'
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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help me with part e and f please
Transcribed Image Text:(b)
(c)
(d)
(e)
(f)
Consider the function
f(x) = |x| over the interval – L≤ x ≤ L.
Derive the Fourier sine series over the interval −L ≤ x ≤ L.
=
= L
Derive the Fourier cosine series over the interval –L ≤ x ≤ L.
Derive the full periodic series over the interval -L ≤ x ≤ L.
For each series computed in parts (a) - (c) what is the value at x
Which of the series in parts (a) - (c) can be differentiated term by
term so that the resulting series converges to the derivative of f(x) with respect
to x over the interval -L≤ x ≤ L?
Which of the series in parts (a) - (c) can be integrated term by term
so that the resulting expression converges to the integral
S* f ( x') dx'
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