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## Homework Statement

Solve u

_{t}+3u

_{x}=0, where -infinity < x < infinity, t>0, and u(x,0)=f(x).

## Homework Equations

Fourier Transform where (U=fourier transform of u)

Convolution Theorem

## The Attempt at a Solution

I've used Fourier transform to get that U

_{t}-3iwU=0 and that U=F(w)e

^{3iwt}. However, I'm completely stuck trying to find the inverse Fourier transform of e

^{3iwt}in order to use the convolution theorem; I suspect that it's a dirac delta function of t-3t, but the table that I'm using doesn't have this general form and contains a 1/2pi constant at the front for the function to be transformed.

Thanks.