The Genesis And Evolution Of Fourier Series

The mathematicians had ever investigated the trigonometric series extensively as early as the 18th century. In the process of studying partial differential equations, the theory of Fourier's trigonometric series arose, and then it brought deep influence on the whole mathematics and promoted greatly the development of mathematics of the 19th century.Centering on the origin and development of Fourier series and according to the changes of idea caused by trigonometric series, the present paper tries to analyze the historical background in which the theory comes into being, on the basis of the primary mathematicians and their work, and summarizes the process of establishment of it and its advancement to the mathematics of the 19th century. I hope that it is useful to the research of Fourier series.This paper consists of three parts and the order of its times is from the middle of the 18 century to the end of this century, from the beginning of the 19th century to 1830, and from 1830 to the end of the 19th century. In Part one on the exploration of trigonometric series in the 18th century, I describe the historical background in which it comes forth. In Part two on the life of Fourier and the birth of his theory, I present his work systematically and thoroughly. In part three on the impact on the whole mathematics, I show that the promotion to development of Fourier's work to mathematics from 4 aspects, including (1)converge and converge uniformly (2)the concept of function (3)integral (4)set theory.