Title: 23.1 Periodic Functions
Course: HELM Workbooks 2023-2024 > Section: HELM 23: Fourier Series

Fourier series are usually infinite series but involve sine and cosine functions (or their complex exponential equivalents) rather than polynomials. They are widely used for approximating periodic functions. Such approximations are of considerable use in science and engineering. For example, elementary a.c. theory provides techniques for analyzing electrical circuits when the currents and voltages present are assumed to be sinusoidal. Fourier series enable us to extend such techniques to the situation where the functions (or signals) involved are periodic but not actually sinusoidal.

Here, we shall recognise periodic functions, and determine the frequency, the amplitude and the period of a sinusoid.