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Advanced Mathematics for Applications by Andrea Prosperetti

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3

Fourier Series: Applications

 

The Fourier series is arguably the most basic tool to deal with partial differential equations in many commonly encountered bounded domains. This series is the simplest embodiment of the general framework of eigenfunction expansions outlined in §2.1, to which the reader may wish to refer to gain a deeper intuitive understanding of the approach and related manipulations. Furthermore, for the reason explained on p. 364, questions of convergence of other series expansions are reducible ultimately to the convergence of the Fourier series.

We start by presenting a summary of the basic relations and then proceed directly to show several applications. The underlying theory is covered in Chapter 9. In the examples ...

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