The use of Fourier series in applications and some of the issues that may arise in such use can be nicely illustrated by solving any of a number of classical problems. We will consider two: a heat flow problem and a vibrating string problem. The first, determining the temperature distribution throughout some heat conducting rod, is basically the same problem Fourier first solved using the series later named for him. The second is the problem of modeling the motion of an elastic string stretched between two points, a problem undoubtedly of interest to all guitar and banjo players.

Since the main goal is to illustrate the use of Fourier series and to examine some of the problems in their use, we will limit ourselves to relatively ...

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