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CzarJ · Hot babe

Normally my Partial Differential Equations class is pretty easy, but I can't seem to get my head around this problem.

I'm supposed to use Fourier transforms, convolutions, Gauss's kernel, and/or the error function to solve the heat equation:

u _t = u _xx , u(x,0) = 70*e ^{-(x^2)/2} .

All I've managed to do is use two different methods to get two different integrals I can't integrate. Any thoughts?

Lepton* · Guest

I have nothing, dude, sorry. Dispirited

Bicho the Inhaler · Daedalian Member

Why don't you post the integral? Chances are, it's the integral of a Gaussian in some form or other.

CzarJ · Hot babe

Good idea--I will, when it's not 1 in the morning and me in my pajamas.

CzarJ · Hot babe

I actually ended up figuring this one out--my stubbornness wouldn't allow me to seek any further help--but Bicho was right, for what it's worth. After a really weird-looking completion of the square and u-substitution, I ended up with the Gaussian. Go figure.