Abstract
In this chapter we will analyze Fourier series in more detail, and show that the Fourier approach yields a general solution for the one-dimensional heat equation. The primary significance of this approach to PDE is the philosophy of spectral analysis that it inspired. The decomposition of functions with respect to the spectrum of a differential operator is a tool with enormous applications, both theoretical and practical.
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Borthwick, D. (2016). Fourier Series. In: Introduction to Partial Differential Equations. Universitext. Springer, Cham. https://doi.org/10.1007/978-3-319-48936-0_8
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DOI: https://doi.org/10.1007/978-3-319-48936-0_8
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Publisher Name: Springer, Cham
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