where Su₁(x, t) = Urr(x, t), [u(x,0) = g(x), 1, g(x) = |0, = TER, t> 0, |x|≤1, x>1.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Represent the solution of the following heat equation as an improper integral using
Fourier transform

Do not evaluate the integral at the end and look closely at your solution, you will see that at t = 0 the temperature is zero everywhere outside of [−1, 1] but at any positive t, the temperature is nowhere zero

where
Su₁(x, t) = Uxx(x, t),
[u(x,0) = g(x),
1,
g(x)
0,
=
TER, t> 0,
|x| ≤ 1,
|x|>1.
Transcribed Image Text:where Su₁(x, t) = Uxx(x, t), [u(x,0) = g(x), 1, g(x) 0, = TER, t> 0, |x| ≤ 1, |x|>1.
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