# Toronto Math Forum

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

Title: Lecture 19
Post 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.
Title: Re: Lecture 19
Post by: Victor Ivrii on November 13, 2012, 03:29:59 PM
No, if you scale $x\mapsto \sigma x$ you scale $\xi \mapsto \sigma^{-1}\xi$ to keep $x\xi$ the same..
Title: Re: Lecture 19
Post by: Miranda Jarvis on December 19, 2012, 11:27:42 AM
Just to clarify, I'm assuming that in the lead up to equation 25 it was meant to be $-|\xi|^{-1}e^{-|\xi|y}$ not $x$ and $i$  . . .
Title: Re: Lecture 19
Post by: Miranda Jarvis on December 19, 2012, 11:53:40 AM
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 . . .
Title: Re: Lecture 19
Post by: Victor Ivrii on December 19, 2012, 12:12:30 PM
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
Title: Re: Lecture 19
Post by: Miranda Jarvis on December 19, 2012, 01:25:42 PM
again, not to be a pain, but is it in fact supposed to be $\xi$ not $xi$ in the lead up to equation 25?
Title: Re: Lecture 19
Post by: Victor Ivrii on December 19, 2012, 02:27:29 PM
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 delimiters--fixed