[944] Typo in question 4(b).
Gautam Iyer
gi1242+944 at cmu.edu
Mon Nov 27 21:54:15 EST 2017
Hi Guys,
There is a typo in Q4(b): I wrote
v(t, y) = e^{\gamma_1 t} c(T - t, y + \gamma_2 (T-t))
This is incorrect. It should instead be
v(t, y) = e^{\gamma_1 t} c(T - t, x e^{\gamma_2 (T-t)} )
Since this was leading to some confusion, I realized that the question
can be stated (and solved) in a simpler way using a conventional
substitution. Namely define new variables
tau = T - t and z = y + gamma_2 tau
and choose gamma_1 and gamma_2 appropriately to get the heat equation
for v (in variables tau and z).
I updated the homework to reflect this.
Best,
Gautam
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