Fourier Series

Mathematicians of the eighteenth century, including Daniel Bernoulli and Leonhard Euler, expressed the problem of the vibratory motion of a stretched string through partial differential equations that had no solutions in terms of “elementary functions.” Their resolution of this difficulty was to introduce infinite series of sine and cosine functions that satisfied the equations. In the early nineteenth century, Joseph Fourier, while studying the problem of heat flow, developed a cohesive theory of such series. Consequently, they were named after him.