The Fourier Transform - Partial Differential Equations | Lecture 34

In the previous lecture we solved the heat equation on an infinite line to see that the solution is written as an integral over all wave numbers. In this lecture we investigate this integral operator, termed the Fourier transform. We derive the Fourier transform as the limit of a Fourier series as the domain becomes unbounded. As an example we show that Gaussians in physical space are transformed to Gaussians in Fourier/frequency space, and vice-versa. This property will be used in the next lecture when identifying the fundamental solution of the heat equation.

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[billworthers]

How is he writing on the blackboard like that?