Fourier series^{1} is an important tool in solving problems in conduction of heat, electrical engineering, current and voltage in alternating circuits, electrodynamics, acoustics, *etc*. The basic idea is to represent periodic functions by a series involving sines and cosines. In this chapter, we find expansion of even/odd functions first in an interval of 2*π* and later of 2*l*. Finally, we develop half-range Fourier series also.

First we begin with the notion of periodic functions; and even and odd functions.

The graph of a trigonometric function repeats itself in regular intervals. Such functions are called periodic functions.

**Periodic Function: Definition** A function *f* (

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