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Essential Mathematical Methods for the Physical Sciences by K. F. Riley, M. P. Hobson

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4

Fourier series

The reader will be familiar with how, through Taylor series (see Section A.6 of Appendix A), complicated functions may be expressed as power series. However, this is not the only way in which a function may be represented as a series, and the subject of this chapter is the expression of functions as a sum of sine and cosine terms. Such a representation is called a Fourier series. Unlike Taylor series, a Fourier series can describe functions that are not everywhere continuous and/or differentiable. There are also other advantages in using trigonometric terms. They are easy to differentiate and integrate, their moduli are easily taken and each term contains only one characteristic frequency. This last point is important because, ...

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