Toronto Math Forum
APM3462012 => APM346 Math => Misc Math => Topic started by: Aida Razi on November 13, 2012, 03:12:17 PM

In heat equation: We know IFT of e^ ((Î¾^2)/2) is (âˆš2pi)e ((x^2)/2). Then when we try to find IFT of e^ ((ktÎ¾^2)), we scale Î¾ to âˆš(2kt)Î¾ and therefore x scale to âˆš(2kt)x. But in the lecture note, it is mentioned that x scale to (2kt)^(1/2)x. I believe it should be just square root of 2kt and not (square root) of 2kt.

No, if you scale $x\mapsto \sigma x$ you scale $\xi \mapsto \sigma^{1}\xi$ to keep $x\xi$ the same..

Just to clarify, I'm assuming that in the lead up to equation 25 it was meant to be $\xi^{1}e^{\xiy}$ not $x$ and $i$ . . .

I'm sorry to nit pick but as someone who is having a hard enough time following much of this material, I was wondering in the lines shown in the screen capture attached (the lead up to equation 39 is there an extra $i$ in the denominator of the first equation? I think this is supposed to be equal to the second term in the right side of equation 38 . . .

I'm sorry to nit pick but as someone who is having a hard enough time following much of this material, I was wondering in the lines shown in the screen capture attached (the lead up to equation 39 is there an extra $i$ in the denominator of the first equation? I think this is supposed to be equal to the second term in the right side of equation 38 . . .
You are correct. Fixed

again, not to be a pain, but is it in fact supposed to be $\xi$ not $xi$ in the lead up to equation 25?

again, not to be a pain, but is it in fact supposed to be $\xi$ not $xi$ in the lead up to equation 25?
You mean after (5)? Yes there were missing math delimitersfixed