Applied Mathematics
Some of Euler's greatest successes were in applying analytic methods to real world problems, describing numerous applications of Bernoulli's numbers, Fourier series, Venn diagrams, Euler numbers, e and π constants, continued fractions and integrals. He integrated Leibniz's differential calculus with Newton's Method of Fluxions, and developed tools that made it easier to apply calculus to physical problems. In particular, he made great strides in improving numerical approximation of integrals, inventing what are now known as the Euler approximations. The most notable of these approximations are Euler method and the Euler–Maclaurin formula. He also facilitated the use of differential equations, in particular introducing the Euler-Mascheroni constant:
One of Euler's more unusual interests was the application of mathematical ideas in music. In 1739 he wrote the Tentamen novae theoriae musicae, hoping to eventually integrate music theory as part of mathematics. This part of his work, however did not receive wide attention and was once described as too mathematical for musicians and too musical for mathematicians.
Read more about this topic: Contributions Of Leonhard Euler To Mathematics
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