Engineering Mathematics

17

Fourier Series

In the early eighteenth century, the work of C. Maclaurin and B. Taylor led to the representation of functions like sin x, cos x, e^x, and arc tan x as power series expansions. By the middle of the eighteenth century it became important to study the possibility of representation of the ‘given function by infinite series other than the power series. Since many phenomena like vibration of string, the voltages and currents in electrical networks, electromagnetic signals, and movement of pendulum are periodic in nature, physicist, and mathematicians discussed the possibility of representing a periodic function as an infinite series involving sinusoidal (sin x and cos x) functions. In his classic Théorie analytique de la chaleur