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.