Fourier Series :: physics fourier

Jean Baptiste Joseph Fourier (March 21, 1768 - May 16, 1830) was a French mathematician and physicist who is best cognize for initiating the investigation of Fourier serial. He was born at Auxerre in the Yonne d federal agencyement of France, the news of a tailor, and was educated by the Benedictines. The commissions in the scientific corps of the regular army were reserved for those of good birth, and being thus ineligible he current 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 make 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 alike contributed several mathematical papers to the Egy ptian Institute which Napoleon founded at Cairo, with a view of weakening English influence in the East. after(prenominal) the British victories and the capitulation of the French under General Menou in 1801, Fourier returned to France, and was do prefect of Isre, 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 Thorie analytique de la chaleur, in which he bases his reasoning on Newtons law of cooling, namely, that the pay heed of heat between two adjacent molecules is proportional to the extremely dispirited difference of their temperatures. In this work he claims that any functions of a variable, whether incessant or discontinuous, can be expanded in a series of sines of multiples of the variable - this result isnt correct at all. But the fact that roughly discontinuous functions are the sum of infinite series was a breakthrough. The interrogative sentence of determine when a function is the sum of its Fourier series has been fundamental for centuries. Lagrange had abandoned particular cases of this (false) theorem, and had implied that the method was general, but he had not pursued the subject. Dirichlet was the firstborn to give a satisfactory demonstration of it, with some restrictive conditions.