astronomy

Ivan Petrovsky

Ivan Petrovsky is a astronomy 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 Ivan Petrovsky rather than just read about it. In short: Ivan Georgiyevich Petrovsky (Russian: Иван Георгиевич Петровский; 18 January 1901 – 15 January 1973) was a Soviet mathematician working mainly in the field of partial differential equations. He greatly contributed to the solution of Hilbert's 19th and 16th problems, and discovered what are now called Petrovsky lacunas.

Key takeaways

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Reference excerpt

Ivan Georgiyevich Petrovsky (Russian: Иван Георгиевич Петровский; 18 January 1901 – 15 January 1973) was a Soviet mathematician working mainly in the field of partial differential equations. He greatly contributed to the solution of Hilbert's 19th and 16th problems, and discovered what are now called Petrovsky lacunas. He also worked on the theories of boundary value problems, probability, and on the topology of algebraic curves and surfaces.

Biography Petrovsky was a student of Dmitri Egorov. Among his students were Olga Ladyzhenskaya, Evgenii Landis, Olga Oleinik and Sergei Godunov. Petrovsky taught at Steklov Institute of Mathematics. He was a member of the Academy of Sciences of the Soviet Union since 1946 and was awarded Hero of Socialist Labour in 1969. He was the president of Moscow State University (1951–1973) and the head of the International Congress of Mathematicians (Moscow, 1966). He died in Moscow, and was buried in the Novodevichy Cemetery.

Selected publications Petrovsky, I. G. (1937), "Über das Cauchysche Problem für Systeme von partiellen Differentialgleichungen", Recueil Mathématique (Matematicheskii Sbornik) (in German), 2 (44) (5): 815–870, JFM 63.0466.03, Zbl 0018.40503. Petrovsky, I. G. (1939), "Sur l'analyticité des solutions des systèmes d'équations différentielles", Recueil Mathématique (Matematicheskii Sbornik) (in French), 5 (47) (1): 3–70, JFM 65.0405.02, MR 0001425, Zbl 0022.22601. Petrovsky, I. G. (1945), "On the diffusion of waves and the lacunas for hyperbolic equations", Recueil Mathématique (Matematicheskii Sbornik), 17 (59) (3): 289–368, MR 0016861, Zbl 0061.21309. Petrovsky, I. G. (1953), Vorlesungen über die Theorie der Integralgleichungen, Würzburg: Physica Verlag Petrovsky, I. G. (1954), Lectures on partial differential equations, New York: Interscience Petrovsky, I. G. (1954), Vorlesungen über der gewöhnlichen Differentialgleichungen, Teubner Petrovsky, I. G. (1957), Lectures on the theory of integral equations, Rochester: Graylock| Petrowsky, I. G. (1996), Oleinik, O. A. (ed.), Selected works. Part I: Systems of partial differential equations and algebraic geometry, Classics of Soviet Mathematics, vol. 5 (part 1), Amsterdam: Gordon and Breach Publishers, ISBN 978-2-88124-978-5, MR 1677652, Zbl 0948.01042. Petrowsky, I. G. (1996), Oleinik, O. A. (ed.), Selected works. Part II: Differential equations and probability theory, Classics of Soviet Mathematics, vol. 5 (part 2), Amsterdam: Gordon and Breach Publishers, ISBN 978-2-88124-979-2, MR 1677648, Zbl 0948.01043.

References

Aleksandrov, P. S.; Arnol'd, V. I.; Gel'fand, I. M.; Kolmogorov, A. N.; Novikov, S. P.; Oleinik, O. A. (2001), "Ivan Georgievich Petrovskii", in Osipov, Yu. S.; Sadovnichii, V. A. (eds.), Differential Equations and Related Topics - dedicated to the 100th Anniversary of I.G. Petrovskii, Moscow: Lomonosov State University and Steklov Mathematical Institute, pp. 1–18, retrieved 1 September 2009. A very ample paper describing Petrovsky's scientific research, authored by friends, collaborators and pupils. Aleksandrov, P. S.; Oleinik, O. A. (1981), "On the eightieth anniversary of the birth of Ivan Georgievich Petrovskii", Uspekhi Matematicheskikh Nauk (in Russian), 36 (1(217)): 3–10, Bibcode:1981RuMaS..36Q...1A, doi:10.1070/rm1981v036n01abeh002539, MR 0608939, S2CID 250833608, Zbl 0454.01022: the original paper translated in (Alexandrov & Oleinik 1996), and also in the Russian Mathematical Surveys, 1981, 36:1, 1–8. Alexandrov, P. S.; Oleinik, O. A. (1996), "Ivan Georgievich Petrowsky", in Oleinik, O. A. (ed.), Selected works. Part II: Differential equations and probability theory, Classics of Soviet Mathematics, vol. 5 (part 2), Amsterdam: Gordon and Breach Publishers, pp. 1–9, ISBN 978-2-88124-979-2, MR 1677648, Zbl 0948.01043: an English translation of the paper (Aleksandrov & Oleinik 1981). Kolmogorov, A. N. (1996), "Ivan Georgievich Petrowsky", in Oleinik, O. A. (ed.), Selected works. Part I: Systems of partial differential equations and algebraic geometry, Classics of Soviet Mathematics, vol. 5 (part 1), Amsterdam: Gordon and Breach Publishers, pp. 1–3, ISBN 978-2-88124-978-5, MR 1677652, Zbl 0948.01042 Lui, S. H. (1997), "An Interview with Vladimir Arnol´d" (PDF), Notices of the American Mathematical Society, 44 (4): 432–438, Zbl 0913.01024. An interview with Vladimir Igorevich Arnol'd containing several important historical details about his teachers and other great mathematicians he knew when he was first studying and then working at the MSU Faculty of Mechanics and Mathematics, including Ivan Petrowsky. Oleinik, O. A. (1996), "I. G. Petrowsky and Modern Mathematics", in Oleinik, O. A. (ed.), Selected works. Part I: Systems of partial differential equations and algebraic geometry, Classics of Soviet Mathematics, vol. 5 (part 1), Amsterdam: Gordon and Breach Publishers, pp. 4–30, ISBN 978-2-88124-978-5, MR 1677652, Zbl 0948.01042 Gårding, L. (1996), "Ivan Georgievich Petrowsky and Partial Differential Equations", in Oleinik, O. A. (ed.), Selected works. Part I: Systems of partial differential equations and algebraic geometry, Classics of Soviet Mathematics, vol. 5 (part 1), Amsterdam: Gordon and Breach Publishers, pp. 31–39, ISBN 978-2-88124-978-5, MR 1677652, Zbl 0948.01042. Vol'pert, A. I. (1996), "Propagation of Waves Described by Nonlinear Parabolic Equations (a commentary on article 6)", in Oleinik, O. A. (ed.), Selected works. Part II: Differential equations and probability theory, Classics of Soviet Mathematics, vol. 5 (part 2), Amsterdam: Gordon and Breach Publishers, pp. 364–399, ISBN 978-2-88124-979-2, MR 1677648, Zbl 0948.01043

External links

Ivan Petrovsky at the Mathematics Genealogy Project O'Connor, John J.; Robertson, Edmund F., "Ivan Petrovsky", MacTutor History of Mathematics Archive, University of St Andrews Short Biography of Petrowsky – from the Moscow Mathematical Journal

Illustrations

Worked examples

Example 1 — a first encounter with Ivan Petrovsky

Start with the simplest possible case. Write down what Ivan Petrovsky claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In astronomy, 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 Ivan Petrovsky 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 Ivan Petrovsky 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 Ivan Petrovsky

In research: Ivan Petrovsky appears in astronomy 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 Ivan Petrovsky 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: Ivan Petrovsky is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1901 births, 1973 deaths, 20th-century Russian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Ivan Petrovsky 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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How to study Ivan Petrovsky in 20 minutes

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Frequently asked questions

What is Ivan Petrovsky in simple terms?

Why does Ivan Petrovsky matter?

Because it connects several astronomy ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Ivan Petrovsky?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

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It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Ivan Petrovsky.