Consider the function f(t) = 0.01e2t for 0 ≤t≤ π). (a) Sketch the even extension, feven, and the odd extension fodd of the function f(t) over the range -37 ≤ t ≤ 3n, clearly indicating each case. (b) Now consider the function g(t) = feven (t) + fodd (t), which has Fourier series G(t) given by 8 ∞ G(t) = A + Σ An cos(nat) + Σ B, sin(nat). B₂ n=1 n=1 Calculate the constant term Ao.
Consider the function f(t) = 0.01e2t for 0 ≤t≤ π). (a) Sketch the even extension, feven, and the odd extension fodd of the function f(t) over the range -37 ≤ t ≤ 3n, clearly indicating each case. (b) Now consider the function g(t) = feven (t) + fodd (t), which has Fourier series G(t) given by 8 ∞ G(t) = A + Σ An cos(nat) + Σ B, sin(nat). B₂ n=1 n=1 Calculate the constant term Ao.
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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Transcribed Image Text:Consider the function f(t) = 0.01e2t for 0 ≤t≤ π).
(a) Sketch the even extension, feven, and the odd extension fodd of the
function f(t) over the range -37 ≤ t ≤ 37, clearly indicating each
case.
(b) Now consider the function g(t) = feven (t) + fodd (t), which has
Fourier series G(t) given by
8
G(t) = Ao +) An
cos(n7t)+
Σ Αn cos(nat) + Σ Bn sin(nat).
B₂
n=1
n=1
Calculate the constant term Ao.
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