Find the temperature in a thin metal rod of length l
with both ends insulated and with initial tempera-
ture in the rod sin (p x/l ).
Solution The initial boundary value problem
consists of the following
1. Partial differential equation for conduction of heat
2
2
2
uu
a
t
x
∂∂
=
∂
∂
(1)
2. Boundary conditions: (Insulation at both ends)
0
0;
x
u
x
=
∂
=
∂
0
xl
u
x
=
∂
=
∂
(2), (3)
3. Initial condition:
(,0)sin
x
ux
l
⎛⎞
=
⎜⎟
⎝⎠
p
(4)
The general solution ...
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