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P. 102
r Z
2 h p
u n (0) = sin( λ n x)f(x) dx ≡ f n
h 0
Thus the temperature is given by
r ∞
2 X p
u(x, t) = u n (t) sin( λ n x),
h
n=1
r Z
2 t p
n
e −κλ nt + κ e −κλ n(t−τ) λ n α(τ) + (−1) β(τ) dτ.
u n (t) = f n
h 0
95
