(adsbygoogle = window.adsbygoogle || []).push({}); Delta Dirac - Question on my final :(

Man I just had this final, and I didn't study the delta function enough. I totally bombed this question. I think I did ok on the rest of it... but I messed up bad on this question. I want to know the answer though.

Solve the heat equation:

[tex] u_t = u_{xx} [/tex] with the initial condition [tex] u_0(x)=\delta(x-a) [/tex] using the fundemental solution:

[tex] u(x,t) = \frac{1}{\sqrt{4\pi t}} \int_{\infty}^{\infty} e^{-(x-y)^2/4t}u_0(y)\,\,dy [/tex]

So all I could remember about the delta function is the identity:

[tex] \int_{\infty}^{\infty} f(x)\delta(x-a) \,\,dx = f(a) [/tex]

What confused me was the dummy variable? How do I account for that? I need some hints how to solve this problem, because I'm lost....

grrr... I'm so mad I missed this.

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# Homework Help: Delta Dirac - Question on my final

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