mathematics

Nikolay Krylov (mathematician, born 1879)

Nikolay Krylov (mathematician, born 1879) is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Nikolay Krylov (mathematician, born 1879) rather than just read about it. In short: Nikolay Mitrofanovich Krylov (Russian: Никола́й Митрофа́нович Крыло́в, Ukrainian: Мико́ла Митрофа́нович Крило́в; 29 November [O.S. 17 November] 1879 – May 11, 1955) 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.

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Reference excerpt

Nikolay Mitrofanovich Krylov (Russian: Никола́й Митрофа́нович Крыло́в, Ukrainian: Мико́ла Митрофа́нович Крило́в; 29 November [O.S. 17 November] 1879 – May 11, 1955) 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 Kyiv 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 Bogolyubov 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

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.

See also Describing function Krylov–Bogolyubov theorem Krylov–Bogoliubov averaging method Krylov–Bogolyubov–Mitropolskiy asymptotic method

References O'Connor, John J.; Robertson, Edmund F., "Nikolay Krylov (mathematician, born 1879)", MacTutor History of Mathematics Archive, University of St Andrews

Worked examples

Example 1 — a first encounter with Nikolay Krylov (mathematician, born 1879)

Start with the simplest possible case. Write down what Nikolay Krylov (mathematician, born 1879) claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Nikolay Krylov (mathematician, born 1879) before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Nikolay Krylov (mathematician, born 1879) ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Nikolay Krylov (mathematician, born 1879)

In research: Nikolay Krylov (mathematician, born 1879) appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Nikolay Krylov (mathematician, born 1879) in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Nikolay Krylov (mathematician, born 1879) is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1879 births, 1955 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Nikolay Krylov (mathematician, born 1879) outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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