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Solve heat equation for the following conditions ut = kuxx t > 0, 0 < x...

Solve heat equation for the following conditions

ut = kuxx t > 0, 0 < x < ∞

u|t=0 = g(x)

ux|x=0 = h(t)

2. g(x) = 1 if x < 1 and 0 if x ≥ 1

h(t) = 0;

for k = 1/2

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