2. First show that for the completely insulated bar
ut = c2uxx; 0 < x < L; t >...
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Mathematics, 01.06.2020 00:58 mccdp55
2. First show that for the completely insulated bar
ut = c2uxx; 0 < x < L; t > 0:
ux(0; t) = 0; t > 0
ux(L; t) = 0; t > 0
u(x; 0) = f(x); 0 < x < L
the separation of variables gives the solution
u(x; t) = A0 + 1 Ancos n x e ( cn )2t
L
n=1 L
X
where
2 Z0 L n x
An = f(x)cos dx; n = 1; 2; 3:::;
L L
then nd the temperature in the bar with L = ; c = 1; and f(x) = x
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