Inverse Fourier Transform

  • #1
Conservation
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Homework Statement


Solve ut+3ux=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 Ut-3iwU=0 and that U=F(w)e3iwt. However, I'm completely stuck trying to find the inverse Fourier transform of e3iwt 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.
 

Answers and Replies

  • #2
blue_leaf77
Science Advisor
Homework Helper
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I suspect that it's a dirac delta function of t-3t
Yes, look at this. But the argument of the delta function will be 3t+x.
 

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