Nikolay Mitrofanovich Krylov

Nikolay Krylov
Born	29 November [O.S. 17 November] 1879 St Petersburg, Russian Empire
Died	May 11, 1955(1955-05-11) (aged 75) Moscow, USSR
Citizenship	Russia  Ukrainian SSR  USSR
Nationality	Russian
Fields	Mathematics
Alma mater	St. Petersburg State Mining Institute
Doctoral students	Nikolay Bogolyubov

Nikolay Mitrofanovich Krylov (Russian: Николай Митрофанович Крылов, Ukrainian: Микола Митрофанович Крилов) (29 November [O.S. 17 November] 1879, St Petersburg, Russian Empire — May 11, 1955, Moscow, USSR) was a Russian and Soviet mathematician known for works on interpolation, non-linear mechanics, and numerical methods for solving equations of mathematical physics.

Biography

Nikolay Krylov graduated from St. Petersburg State Mining Institute in 1902. In the period from 1912 until 1917, he held the Professor position in this institute. In 1917, he went to the Crimea to become Professor at the Crimea University. He worked there until 1922 and then moved to Kiev to become chairman of the mathematical physics department at the Ukrainian Academy of Sciences.

Nikolay Krylov was a member of the Société Mathématique de France and the American Mathematical Society.

Research

Nikolay Krylov developed new methods for analysis of equations of mathematical physics, which can be used not only for proving the existence of solutions but also for their construction. Since 1932, he worked together with his student Nikolay Bogoliubov on mathematical problems of non-linear mechanics. In this period, they invented certain asymptotic methods for integration of non-linear differential equations, studied dynamical systems, and made significant contributions to the foundations of non-linear mechanics. They proved the first theorems on existence of invariant measures known as Krylov-Bogolyubov theorems, introduced the Krylov-Bogoliubov averaging method and, together with Yurii Mitropolskiy, developed the Krylov-Bogoliubov-Mitropolskiy asymptotic method for approximate solving equations of non-linear mechanics.

Doctoral students

• Nikolay Bogolyubov

See also

• Describing function
• Krylov-Bogolyubov theorem
• Krylov-Bogoliubov averaging method
• Krylov-Bogoliubov-Mitropolskiy asymptotic method

Publications

Nikolay Krylov published over 200 papers on analysis and mathematical physics and two monographs:

• Nicolas Kryloff (1931): Les Méthodes de Solution Approchée des Problèmes de la Physique Mathématique. Paris: Gauthier-Villars [in French].
• N. M. Krylov, N. N. Bogoliubov (1947): Introduction to Nonlinear Mechanics. Princeton: Princeton University Press. ISBN 978-0-691-07985-1.

References

External links

• Nikolai Krylov at MacTutor biography

Persondata
Name	Krylov, Nikolay Mitrofanovich
Alternative names
Short description
Date of birth	1879-11-29
Place of birth	St Petersburg, Russian Empire
Date of death	1955-05-11
Place of death	Moscow, USSR