Consider the Boundary-Initial Value problem where bn = and 8²u u 0 0 8.x² It u(6, 1) = 0, t>0 u(0, t) = 0, u(x,0) = x(6x), 0

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.3: Maxima And Minima
Problem 1YT
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Consider the Boundary-Initial Value problem
where
bn =
and
3
C₂ =
8²u Ou
8.x² It
0<x<6, t> 0
u(0, t) = 0,
u(6, 1) = 0, t>0
u(x,0) = x(6x), 0<x<6
This models a heated wire, with zero endpoints temperatures. The solution z(x, t) of the initial-boundary value problem is given by the series
b₁, sin((2n-1))
=
u(x, t) =
8
Σb,
n=1
e
Transcribed Image Text:Consider the Boundary-Initial Value problem where bn = and 3 C₂ = 8²u Ou 8.x² It 0<x<6, t> 0 u(0, t) = 0, u(6, 1) = 0, t>0 u(x,0) = x(6x), 0<x<6 This models a heated wire, with zero endpoints temperatures. The solution z(x, t) of the initial-boundary value problem is given by the series b₁, sin((2n-1)) = u(x, t) = 8 Σb, n=1 e
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