Mikhail Ostrogradsky
   HOME

TheInfoList



OR:

Mikhail Vasilyevich Ostrogradsky (transcribed also ''Ostrogradskiy'', Ostrogradskiĭ) (russian: Михаи́л Васи́льевич Острогра́дский, ua, Миха́йло Васи́льович Острогра́дський; 24 September 1801 – 1 January 1862) was a
Ukrainian Ukrainian may refer to: * Something of, from, or related to Ukraine * Something relating to Ukrainians, an East Slavic people from Eastern Europe * Something relating to demographics of Ukraine in terms of demography and population of Ukraine * So ...
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
, mechanician and
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate caus ...
of
Ukrainian Cossack The Cossacks , es, cosaco , et, Kasakad, cazacii , fi, Kasakat, cazacii , french: cosaques , hu, kozákok, cazacii , it, cosacchi , orv, коза́ки, pl, Kozacy , pt, cossacos , ro, cazaci , russian: казаки́ or ...
ancestry. Ostrogradsky was a student of Timofei Osipovsky and is considered to be a disciple of
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
, who was known as one of the leading mathematicians of Imperial Russia.


Life

Ostrogradsky was born on 24 September 1801 in the village of Pashennaya (at the time in the Poltava Governorate,
Russian Empire The Russian Empire was an empire and the final period of the Russian monarchy from 1721 to 1917, ruling across large parts of Eurasia. It succeeded the Tsardom of Russia following the Treaty of Nystad, which ended the Great Northern War. ...
, today in
Kremenchuk Raion Kremenchuk Raion ( uk, Кременчуцький район; Romanization of Ukrainian, translit.: ''Kremenchutskyi raion'') is a raion (district) in Poltava Oblast of central Ukraine. The raion's Capital (political), administrative center is the ...
,
Poltava Oblast Poltava Oblast ( uk, Полта́вська о́бласть, translit=Poltavska oblast; also referred to as Poltavshchyna – uk, Полта́вщина, literally 'Poltava Country') is an oblast (province) of central Ukraine. The administrative ...
,
Ukraine Ukraine ( uk, Україна, Ukraïna, ) is a country in Eastern Europe. It is the second-largest European country after Russia, which it borders to the east and northeast. Ukraine covers approximately . Prior to the ongoing Russian inv ...
). From 1816 to 1820, he studied under Timofei Osipovsky (1765–1832) and graduated from the Imperial University of Kharkov. When Osipovsky was suspended on religious grounds in 1820, Ostrogradsky refused to be examined and he never received his Ph.D. degree. From 1822 to 1826, he studied at the Sorbonne and at the Collège de France in
Paris, France Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), ma ...
. In 1828, he returned to the Russian Empire and settled in
Saint Petersburg Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
, where he was elected a member of the Academy of Sciences. He also became a professor of the Main military engineering School of the Russian Empire. Ostrogradsky died in
Poltava Poltava (, ; uk, Полтава ) is a city located on the Vorskla River in central Ukraine. It is the capital city of the Poltava Oblast (province) and of the surrounding Poltava Raion (district) of the oblast. Poltava is administratively ...
in 1862, aged 60. The
Kremenchuk Mykhailo Ostrohradskyi National University Kremenchuk Mykhailo Ostrohradskyi National University ( uk, Кременчуцький національний університет імені Михайла Остроградського) is a university in Kremenchuk, Ukraine, the larges ...
in
Kremenchuk Kremenchuk (; uk, Кременчу́к, Kremenchuk ) is an industrial city in central Ukraine which stands on the banks of the Dnipro River. The city serves as the administrative center of the Kremenchuk Raion (district) in Poltava Oblast (pr ...
,
Poltava oblast Poltava Oblast ( uk, Полта́вська о́бласть, translit=Poltavska oblast; also referred to as Poltavshchyna – uk, Полта́вщина, literally 'Poltava Country') is an oblast (province) of central Ukraine. The administrative ...
, as well as ''Ostrogradsky street'' in
Poltava Poltava (, ; uk, Полтава ) is a city located on the Vorskla River in central Ukraine. It is the capital city of the Poltava Oblast (province) and of the surrounding Poltava Raion (district) of the oblast. Poltava is administratively ...
, are named after him.


Work

He worked mainly in the mathematical fields of
calculus of variations The calculus of variations (or Variational Calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions t ...
,
integration Integration may refer to: Biology *Multisensory integration *Path integration * Pre-integration complex, viral genetic material used to insert a viral genome into a host genome *DNA integration, by means of site-specific recombinase technology, ...
of algebraic functions,
number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777 ...
,
algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...
,
geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...
,
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
and in the fields of
applied mathematics Applied mathematics is the application of mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical s ...
,
mathematical physics Mathematical physics refers to the development of mathematics, mathematical methods for application to problems in physics. The ''Journal of Mathematical Physics'' defines the field as "the application of mathematics to problems in physics and t ...
and
classical mechanics Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical ...
. In the latter, his key contributions are in the
motion In physics, motion is the phenomenon in which an object changes its position with respect to time. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, speed and frame of reference to an observer and mea ...
of an
elastic body In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are ap ...
and the development of methods for integration of the equations of dynamics and fluid power, following up on the works of
Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
, Joseph Louis Lagrange, Siméon Denis Poisson and Augustin Louis Cauchy. In Russia, his work in these fields was continued by Nikolay Dmitrievich Brashman (1796–1866),
August Yulevich Davidov August Yulevich Davidov (russian: Август Юльевич Давидов) (December 15, 1823 – December 22, 1885) was a Russian mathematician and engineer, professor at Moscow University, and author of works on differential equations with pa ...
(1823–1885) and especially by
Nikolai Yegorovich Zhukovsky Nikolay Yegorovich Zhukovsky ( rus, Никола́й Его́рович Жуко́вский, p=ʐʊˈkofskʲɪj;  – March 17, 1921) was a Russian scientist, mathematician and engineer, and a founding father of modern aero- and hydrodyn ...
(1847–1921). Ostrogradsky did not appreciate the work on non-Euclidean geometry of
Nikolai Lobachevsky Nikolai Ivanovich Lobachevsky ( rus, Никола́й Ива́нович Лобаче́вский, p=nʲikɐˈlaj ɪˈvanəvʲɪtɕ ləbɐˈtɕɛfskʲɪj, a=Ru-Nikolai_Ivanovich_Lobachevsky.ogg; – ) was a Russian mathematician and geometer, kn ...
from 1823 and he rejected it, when it was submitted for publication in the Saint Petersburg Academy of Sciences.


Divergence theorem

In 1826, Ostrogradsky gave the first general proof of the
divergence theorem In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the vol ...
, which was discovered by
Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiarational function In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rat ...
s and . is well known. First, we separate the rational part of the integral of a fractional rational function, the sum of the rational part (algebraic fraction) and the transcendental part (with the
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...
and the
arctangent In mathematics, the inverse trigonometric functions (occasionally also called arcus functions, antitrigonometric functions or cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Spec ...
). Second, we determine the rational part without integrating it and we assign a given integral in Ostrogradsky's form: : \int \, dx = + \int \, dx, where P(x),\, S(x),\, Y(x) are known polynomials of degrees ''p'', ''s'', ''y'' respectively, R(x) is a known polynomial of degree not greater than p - 1, and T(x),\, X(x) are unknown polynomials of degrees not greater than s - 1 and y - 1 respectively. Third, S(x) is the greatest common divisor of P(x) and P'(x). Fourth, the denominator of the remaining integral Y(x) can be calculated from the equation P(x) = S(x)\,Y(x). When we differentiate both sides of the equation above we will get
R(x) = T'(x)Y(x) - T(x)H(x) + X(x)S(x) where H(x) = It can be shown that H(x) is polynomial


See also

* Gauss-Ostrogradsky theorem *
Green's theorem In vector calculus, Green's theorem relates a line integral around a simple closed curve to a double integral over the plane region bounded by . It is the two-dimensional special case of Stokes' theorem. Theorem Let be a positively orient ...
*
Ostrogradsky instability In applied mathematics, the Ostrogradsky instability is a feature of some solutions of theories having equations of motion with more than two time derivatives (higher-derivative theories). It is suggested by a theorem of Mikhail Ostrogradsky in cla ...


Notes


References

*. *. *


External links

* * {{DEFAULTSORT:Ostrogradsky, Mikhail Vasilievich 1801 births 1862 deaths People from Poltava Oblast People from Kobelyaksky Uyezd Ukrainian mathematicians Mathematicians from the Russian Empire 19th-century mathematicians from the Russian Empire Physicists from the Russian Empire National University of Kharkiv alumni University of Paris alumni Members of the French Academy of Sciences Full members of the Saint Petersburg Academy of Sciences Academic staff of Military Engineering-Technical University Privy Councillor (Russian Empire)