Periodic Functions and the Laplace Transform

Watch the Intro to the Laplace Transform in my Differential Equations playlist here:    • Laplace Transforms and Solving ODEs  

We've seen previously in the playlist that Laplace Transforms work great with piecewise functions, functions that have discontinuities in them like the Heaviside or unit step function. In this video we're going to see that it also plays really nicely with periodic functions where f(t+p)=f(t). Indeed, you can always extend a function on an interval to a periodic function on the entire real line and we will have a nice formula from the Laplace Transform to deal with that. This is particularly useful for solving Ordinary Differential Equations (ODE) that have a periodic nonhomogeneity.

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This video was created by Dr. Trefor Bazett. I'm an Assistant Teaching Professor at the University of Victoria.

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