Euler, Leonhard (1707-83)
Mathematician, born in Basel, Switzerland. He studied mathematics there under Jean Bernoulli, and became professor of physics (1731) and then of mathematics (1733) at the St. Petersburg Academy of Sciences. In 1738 he lost the sight of one eye. In 1741 he moved to Berlin as director of mathematics and physics in the Berlin Academy, but returned to St. Petersburg in 1766, soon afterwards losing the sight of his other eye. He was a giant figure in 18th-c mathematics, publishing over 800 different books and papers, on every aspect of pure and applied mathematics, physics and astronomy. His Introductio in analysin infinitorum (1748) and later treatises on differential and integral calculus and algebra remained standard textbooks for a century and his notations, such as e and (pi) have been used ever since. For the princess of Anhalt-Dessau he wrote Lettres à une princesse d'Allemagne (1768-72), giving a clear non-technical outline of the main physical theories of the time. He had a prodigious memory, which enabled him to continue mathematical work and to compute complex calculations in his head when he was totally blind. He is without equal in the use of algorithms to solve problems.
Euler, Leonhard (1707-83)
The gratest mathematician of the eighteenth century, Leonhard Euler (1707-1783), grew up near Basel and was a student of Johann Bernoulli. He followed his friend Daniel Bernoulli to St. Petersburg in 1727. For the remainder of his life he was associated with the St. Petersburg Academy (1727-1741 and 1766-1783) and the Berlin Academy (1741-1766). Euler was the most prolific mathematician of all time; his collected works fill more than 70 large volumes. His intrests ranged over all areas of mathematics and many fields of application. Even though he was blind during the last 17 years of his life, his work continued undiminished until thevery day of his death. Of particular intrest here is his formulation of problems in mechanics in mathematical language and his development of methods of solving these mathematical problems. Lagrange said of Euler's work in mechanics, "The first great work in which analysis is applied to the science of movement." Among other things, Euler identified the condition for exactness of first order differential equations in 1734-35, developed the theory of integrating factors in the same paper, and gave the general solution of homogenous linear equations with constant coefficients in 1743. He extended the latter results to nonhomogenous equations in 1750-51. Beginning about 1750, Euler made frequent use of power series in solving differential equations. He also proposed a numerical procedure in 1768-69, made important contributions in partial differential equations, and gave the first systematic treatment of the calculus of variations.
Boyce, Willian E. and DiPrima, Richard C., Elementary Differential Equations and Boundry Value Problems (5th ed.) (USA: Wiley, 1986)
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