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EULER Leonhard (Euler Leonard)

( German and Russian mathematician, engineer and physicist.)

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Biography EULER Leonhard (Euler Leonard)
Born April 15, 1707 in Basel. He studied at the University of Basel (1720-1724), where his teacher was Johann Bernoulli. In 1722 received a Master of Arts. In 1727 he moved to St. Petersburg, having a place adjunct professor in the newly founded Academy of Sciences and Arts. In 1730 he became a professor of physics in 1733 - Professor of Mathematics. Over 14 years of his first stay in St. Petersburg Euler published over 50 papers. In 1741-1766 he worked in the Berlin Academy of Sciences under the special patronage of Frederick II, and wrote numerous works, covering essentially all sections of Pure and Applied Mathematics. In 1766 at the invitation of Catherine II Euler returned to Russia. Shortly after arriving in St. Petersburg completely lost his vision due to cataracts, . but thanks to excellent memory and ability to carry out calculations in his mind before the end of life engaged in scientific research: During this time they were published nearly 400 papers, . The total number exceeds 850,
. Euler died in St. Petersburg on Sept. 18, 1783.
Proceedings of Euler showed unusual versatility of the author. Widely known for his treatise on celestial mechanics theory of motion of the planets and comets (Theoria motus planetarum et cometarum, 1774), in which special attention is paid to the theory of motion of the Moon. Author of books on hydraulics, shipbuilding, artillery. In 1739, Euler creates a new theory of music. An example of the popularization of science is to present the Euler most important problems of natural science in his Letters to a German Princess on various metaphysical stuffs (Lettres a une Princesse d'Allemagne, 1768-1772). Job doctrine of improvement of glass ophthalmic lenses (Sur la Perfection des Verres Object des Lunettes, 1747) contributed to the creation of achromatic telescopes.

The most famous Euler brought research in the field of pure mathematics. Modern trigonometry with the definition of trigonometric functions as relations with the notation adopted in it goes back to Euler Introduction to the analysis of infinite (Introductio in analysin infinitorum, 1748). In this treatise is given expansion in infinite series of many elementary functions, including ex, sin x, cos x, and displayed a well-known formula (the formula of Euler). When x = p, it gives expression, symbolizing the unity of arithmetic (which brought the numbers 0 and 1), algebra (imaginary number, denoted by i), geometry (the number of p) and analysis (e). Taken in this work an analysis of curves and surfaces using their equations allows us to consider it as the first textbook of analytic geometry.

The next significant essay Euler - Differential Calculus (Institutiones calculi differentialis, 1755), and then three-volume Integral Calculus (Institutiones calculi integralis, 1768-1774). It is not only considered branches of mathematics, made in the names of books, but also develops the theory of ordinary differential equations, partial differential equations. Euler belongs to the first presentation of the calculus of variations, it is the creator of the theory of special functions, are known to work on the theory of numbers. Euler established some properties of analytic functions, applied the imaginary values for evaluating integrals, thus giving rise to complex variable theory.

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