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Visualizing Odd/Even Extensions of Fourier Series

Applet Instructions

Given a function defined on a non-symmetric interval we can construct a Fourier sine series or a Fourier cosine series. These constructions are usually used in solving PDEs where different boundary conditions apply, but they are related to different extensions of the function to the interval . In this applet you can see how the Fourier sine and cosine series relate to even and odd extensions of the given function . You can choose your own function and interval . Click the checkboxes to toggle the visibility of the even or odd extensions of , and the partial Fourier sine and Fourier cosine series of . Change the number of terms in the Fourier expansions by using the slider for .