Leonhard Euler essay

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Leonhard Euler was a Swiss mathematician who made an outstanding contribution to various disciplines such as logics, physics, and mathematics including trigonometry and analytic geometry (Bashmakova, 1988). Moreover, he greatly contributed to the fields of graph theory and infinitesimal calculus. Leonhard Euler was also a member of the Imperial Academy of Sciences.

Euler was born to the family of a pastor in Basel on April 15, 1707. First years of his life he spent in Reihen. As he was a child, his father provided him with basic mathematical instructions, which he later extended engaging in mathematics as a student. Europe’s foremost mathematician Jacob Bernoulli can be considered a mathematical mentor of the young Euler (Finkel 1897). Initially, Euler did not realize at first that mathematics would become a primary discipline and his lifework. After joining University of Basel, Switzerland, in 1720’s, Euler’s mathematical skills were discovered by Bernoulli, an experienced mathematician, who inspired Leonhard to study mathematics, although his father encouraged Euler to become a pastor (Vischer 1987). Consequently, in 1726, Leonhard Euler finished his dissertation De Sono which dealt with the propagation of sound.

In 1727, Euler took part in competition of Paris Academy; he had to discover the best possible ways to place the masts on the ship. At this competition Euler won the second place. The winner was Pierre Bouguer later known as the central figure of naval architecture. Later in his career, Euler scored this prize 12 times (Calinger 1996).

Euler greatly contributed to astronomy and physics. In 1757, he created a number of equations for viscid flow known as Euler equations. Moreover, he argued Newton's theory of light, considered primary at that time. He wrote number of papers on optics in 1740s supporting Huygens’ wave theory of light which consequently became primary (Home 1988).

Euler’s contribution led to the understanding of analysis with regards to the problems of astronomy and physics. His works and ideas have been adopted by many mathematicians and have been extremely essential in studies of the evolutionary effect which formed the basis for the discovery of logarithms (Fraser 1995).
Euler achieved great success solving problems analytically. He also described numerous applications of the Fourier series, Bernoulli numbers, Venn diagrams, the constants e and π, Euler numbers, and continued integrals and fractions. Euler created and introduced a lot of the mathematical terminology used nowadays in the field of mathematical analysis, e.g. mathematical function (Dunham 1999). Euler became the first to apply a mathematical term “function”, which was later defined by Leibniz in 1964 (Wilson 1992).

Euler managed to integrate differential calculus of Leibniz with the method of fluxions (Newton) and developed various tools that helped in applying calculus to physical problems (Calinger 1996). Basically, Euler changed the face of the integral calculus. He is solely responsible for the general solution of linear equations providing vital formulas for approximations. Euler contributed to a great number of discoveries that lead to the union of pure physics and sublime geometry (Hammer & Shin 1996). Euler improved the numerical approximation of integrals by inventing what are nowadays known as the Euler approximations. The most important of these approximations are the Euler–Maclaurin formula and Euler's method. Besides, he made the use of differential equations easier by introducing the Euler–Mascheroni constant: .

All in all, Leonhard Euler is considered one of the greatest mathematicians and scientists of all times. Euler’s works dominated the 19th century mathematics and contributed to the deductions of several features of modern calculus. His works present great and unique contributions to broad mathematical and scientific interest. His works display an original way of solving the mathematical, physical and logical problems (Cannon & Dostrovsky 1981). He earned profound appreciation of other scientists who followed in his footsteps. This brilliant mathematician is chiefly known and remembered as a leading figure in mathematics and science in general during his times with his works noteworthy contributing to physics, astronomy, and engineering.

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