Just as DFT is a stepping stone to Fourier series, Fourier series is a stepping stone to Fourier transform. We arrive at the latter by taking a certain limit of a Fourier expansion of a function. We then show how to solve linear ODE with constant coefficients using the Fourier transform. More importantly, we show that all information about solutions of such ODE is encoded in transfer functions. Finding transfer functions is often the main goal of modeling. We give examples of computation for a circuit and a mass-spring system. We also show how to solve the heat equation on a line using the Fourier transform. Finally, we pay homage to Laplace transform which is closely related to Fourier transform and is very popular in engineering.