Author Topic: Properties of fourier transforms  (Read 110 times)

Shaghayegh A

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Properties of fourier transforms
« on: December 10, 2016, 02:55:06 PM »
I'm stuck on Problem 7 of the 2015 S final exam: http://forum.math.toronto.edu/index.php?topic=606.0    (link also includes prof's solution)

He gets $$\begin{equation*} \hat{u}(k,t)=-ik (2\pi)^{-1} e^{-k^2a^2 /2} \end{equation*}$$ and he's trying to solve for u(x,t). I don't understand how he gets u(x,t); I know he's using the properties of fourier transforms, but I don't know how to go backward from the fourier transform to the inverse fourier transforms! Thanks