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Abstract
Fourier series and general ‘Orthogonal function expansions’ are important in the study of heat flow and wave propagation as well as in pure mathematics. The reason that these series are important is that sines and cosines satisfy the ‘heat equation’ or ‘wave equation’ or ‘Laplace's equation’ for certain geometries of the domain. A general solution of these partial differential equations can sometimes be approximated by a series of the simple solutions by using superposition. We begin the background on series with this topic, because Fourier series provide many interesting examples of delicately converging series.
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