Fourier Series :: physics fourier

Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best known for initiating the investigation of Fourier series. He was born at Auxerre in the Yonne dà ©partement of France, the son of a tailor, and was educated by the Benedictines. The commissions in the scientific corps of the army were reserved for those of good birth, and being thus ineligible he accepted a military lectureship on mathematics. He took a prominent part in his own district in promoting the revolution, and was rewarded by an appointment in 1795 in the Normal school, and subsequently by a chair in the Polytechnic school. Fourier went with Napoleon on his Eastern expedition in 1798, and was made governor of Lower Egypt. Cut off from France by the English fleet, he organized the workshops on which the French army had to rely for their munitions of war. He also contributed several mathematical papers to the Egyptian Institute which Napoleon founded at Cairo, with a view of weakening English influence in the East. After the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France, and was made prefect of Isà ¨re, and it was while there that he made his experiments on the propagation of heat. He moved to Paris in 1816. In 1822 he published his Thà ©orie analytique de la chaleur, in which he bases his reasoning on Newton's law of cooling, namely, that the flow of heat between two adjacent molecules is proportional to the extremely small difference of their temperatures. In this work he claims that any functions of a variable, whether continuou s or discontinuous, can be expanded in a series of sines of multiples of the variable - this result isn't correct at all. But the fact that some discontinuous functions are the sum of infinite series was a breakthrough. The question of determine when a function is the sum of its Fourier series has been fundamental for centuries. Lagrange had given particular cases of this (false) theorem, and had implied that the method was general, but he had not pursued the subject. Dirichlet was the first to give a satisfactory demonstration of it, with some restrictive conditions.