[944] Confusing notations

[Ze Yang]

Hello Professor,

In Homework 4-(b), you let [image: v(t,y)=e^{\gamma_1 t}c(T-t,
y+\gamma_2(T-t))], i.e. treat [image: v] as a function of [image: y=log(x)]
and [image: t].

I think what people usually do for this step is to regard [image: v] as a
function of [image: t, z], with [image: z=y+\gamma_2(T-t)]. And conclude
that [image: v(t,z)] satisfies heat equation [image: \partial_t v = \kappa
\partial_{zz}v].

With your notation, It appears to me that we actually didn't substitute any
variable in this step, and I'm very confused with these notations. Could
you explain?

Thanks!
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