sábado, 1 de dezembro de 2007

Joseph-Louis Lagrange

Joseph-Louis, comte de Lagrange, born Giuseppe Lodovico Lagrangia (January 25, 1736 Turin, Kingdom of Sardinia - April 10, 1813 Paris) was an Italian / French mathematician and astronomer who made important contributions to all fields of analysis and number theory and to classical and celestial mechanics as arguably the greatest mathematician of the 18th century. It is said that he was able to write out his papers complete without a single correction required. Before the age of 20 he was professor of geometry at the royal artillery school at Turin. By his mid-twenties he was recognized as one of the greatest living mathematicians because of his papers on wave propagation and the maxima and minima of curves. His greatest work, Mécanique Analytique (Analytical Mechanics) (4. ed., 2 vols. Paris: Gauthier-Villars et fils, 1888-89. First Edition: 1788), was a mathematical masterpiece and the basis for all later work in this field. On the recommendation of Euler and D'Alembert, Lagrange succeeded the former as the director of mathematics at the Prussian Academy of Sciences in Berlin. Under the First French Empire, Lagrange was made both a senator and a count; he is buried in the Panthéon.
It was Lagrange who created the
calculus of variations which was later expanded by Weierstrass, solved the isoperimetrical problem on which the variational calculus is in part based, and made some important discoveries on the tautochrone which would contribute substantially to the then newly formed subject. Lagrange established the theory of differential equations, and provided many new solutions and theorems in number theory, including Wilson's theorem. Lagrange's classic Theorie des fonctions analytiques laid some of the foundations of group theory, anticipating Galois. Lagrange developed the mean value theorem which led to a proof of the fundamental theorem of calculus, and a proof of Taylor's theorem. Lagrange also invented the method of solving differential equations known as variation of parameters, applied differential calculus to the theory of probabilities and attained notable work on the solution of equations. He studied the three-body problem for the Earth, Sun, and Moon (1764) and the movement of Jupiter’s satellites (1766), and in 1772 found the special-case solutions to this problem that are now known as Lagrangian points. But above all he impressed on mechanics, having transformed Newtonian mechanics into a branch of analysis, Lagrangian mechanics as it is now called, and exhibited the so-called mechanical "principles" as simple results of the variational calculus.

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