mikhail vasilievich ostrogradsky

Mikhail Vasilievich Ostrogradsky (transcribed also Ostrogradskii, Ostrogradskiĭ) (Михаил Васильевич Остроградский) (September 24 1801 - January 1 1862) was a Ukrainian mathematician, mechanician and physicist. Ostrogradsky is considered to be Leonhard Euler's disciple and the leading Russian mathematician of that day. Ostrogradsky was born in Pashennaya (Пашенная), Imperial Russia (now Ukraine). From 1816 to 1820 he studied under Timofei Fedorovich Osipovsky (1765-1832) and graduated from the University of Kharkov. When 1820 Osipovsky was suspended on religious base, Ostrogradsky refused to be examined and he never received his Doctors degree. From 1822 to 1826 he studied at the Sorbonne and at the Collge de France in Paris, France. In 1828 he returned to St. Petersburg, where he was elected as a member of the Academy of Sciences. He worked mainly in the mathematical fields of calculus of variations, integration of algebraic functions, number theory, algebra, geometry, probability theory and in the fields of mathematical physics and classical mechanics. In the latter his most important work includes researches of the motion of an elastic body and the development of methods for integration of the equations of dynamics. Here he continued works of Euler, Joseph Louis Lagrange, Simon-Denis Poisson and Augustin Louis Cauchy. His work in these fields was in Russia continued by Nikolay Dmitrievich Brashman (1796-1866), August Yulevich Davidov (1823-1885) and specially by the brilliant work of Nikolai Yegorovich Zhukovsky (1847-1921). Ostrogradsky did not appreciate the work on non-euclidean geometry of Nikolay Ivanovich Lobachevsky from 1823 and he rejected it, when it was submitted for publication in the St. Petersburg Academy of Sciences. His method for integrating the rational functions is well known. With his equation we separate integral of a fractional rational function, the sum of the rational part (algebraic fraction) and the trancendental part (with the logarithm and the arc tangent). We determine the rational part without integrating it and we assign a given integral into Ostrogradsky's form:

\int {R(x)\over P(x)} dx = {T(x)\over S(x)} + \int {X(x)\over Y(x)} dx \; ,

where P(x), S(x), Y(x) are known polynomials of degrees p, s and y, R(x) known polinomial of degree not greater than p-1, T(x) and X(x) unknown polinomials of degrees not greater than s-1 and y-1 respectively. Ostrogradsky died in Poltava (Полтава), Imperial Russia, now Ukraine. See also:

Divergence theorem (Ostrogradsky-Gauss theorem / Gauss-Ostrogradsky // Green-Ostrogradsky-Gauss / Gauss-Green-Ostrogradsky)

Ostrogradsky's equation