f(t) = t(1 – t), on 0

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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Question
f(t) = t(1 – t),
on 0<t< 1
a) Find the Fourier Sine Series expansion and the Fourier Cosine Series expansion of
given function.
b) Use your Fourier expansions to show that
- 1k
Lk=1 k²
i)
12
- 1k
ii) EK-1
00
%3|
2k=1
(2k-1)2
32
Transcribed Image Text:f(t) = t(1 – t), on 0<t< 1 a) Find the Fourier Sine Series expansion and the Fourier Cosine Series expansion of given function. b) Use your Fourier expansions to show that - 1k Lk=1 k² i) 12 - 1k ii) EK-1 00 %3| 2k=1 (2k-1)2 32
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