This is a 30 minute screencast I made that shows some ways to use Sage ( to illustrate Fourier series and some of their applications. Some applications included are approximating a waveform for a flute and solving the heat equation of a wire using Fourier's method.

The screencast follows a Sage worksheet. The Sage worksheet is available from and (as a pdf only) from

You can download Sage from It is a cross-platform free, open-source mathematics software program similar to the (expensive commercial programs) Mathematica, Maple or Matlab.

This screen-cast and the sws worksheet are both licensed under the Creative Commons 3.0 BY-SA license.

Feel free to re-use and redistribute.

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