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Right now you can make a small digression into the history
of basic subjects which are traditionally taught at the Mathematical Physics Equations
Department in Classical universities.
Mathematical Physics is a pure mathematical science indeed,
it differs from Geometry as it is based on the knowledge of nature not axioms. Archimedes,
an ancient scientist and warrior (282-212 B.C.) is truly considered to be the founder of
the Mathematical Physics Equations. It was he who discovered a number of physical laws
such as the law of a lever, the law of floating of bodies and others and Archimedes used
them successfully not only in practice but also in mathematical constructions.
Mathematical Physics got a mighty impulse in the XVIII
century after I. Newton (1643-1727) and G. Leibniz (1646-1716) had invented the
methods of Mathematical analyses. The works of the Pleiades of outstanding scientists
J. Bernoulli (1700-1782), L. Euler (1707-1783), G. d’Alembert
(1717-1783), G. Lagrange (1736-1813), P. Laplace, G. Fourier (1768-1830),
S. Poisson (1781-1840) put basis for the theory of classical mathematical physics
equation typical representatives of which are the equations of heat-conducting, wave
equations and the equations of Laplace and Poisson.
In the XIX century the equations of mathematical physics
got a solid basis due to the development of methods of analyses and grounding mathematical
analysis. In theories apart from the formulas giving the solutions of the equations in
important but particular cases the results of the analytical character appear such as the
theorem about the existence of solutions, the principle of maximum and others. Thanks to
the brilliant works of mathematicians of that time A. Cauchy (1789-1857),
L. Dirichlet (1805-1859), K. Weierstrass (1815-1897),
S. V. Kovalevskaya (1850-1891) the new theory of the equations with particular
derivatives singled out from mathematical physics.
In the XXth century the equations with particular
derivatives having experienced beneficial influence of the arising mathematical theories
(harmonical and functional analyses, the theory of Lie groups and others) change into a
very strong and branching science, which is in the appendices of different branches of
natural science. This particular science made it possible the flight of a man into space
(Yu. A. Gagarin, 1961) and landing people on the Moon (N. Armstrong,
A. Oldrin, 1969). Nowadays the theory of equations with particular derivatives is an
inalienable part of classical university education in the field of mathematics,
information science and physics.
Let’s call the names of the outstanding Russian
mathematicians whose fundamental works of the world level made up the basis of modern
subjects of the profile of the department. They are I. G. Petrovsky (1901-1973)
and O. A. Oleinik (1925-2001), V. I. Smirnov (1887-1974) and
O. A. Ladyzchenskaya (1922-2004), A. N. Tikhonov (1906-1993) and
A. A. Samarsky (1919-2008).
In the late XIX – early XX century in the writings of
H. Poincare (1854-1912), C. G. Rossby (1898-1957), and many others began to
appear non-classical equations of mathematical physics. Their systematic study began in
the fundamental work of Sobolev (1908-1989) in the mid 50's of the last century.
Currently, especially the rapidly developing one of the domains of non-classical equations
of mathematical physics – the Sobolev type equations. In Russia, this direction is
represented by G. V. Demidenko, N. A. Sidorov,
M. V. Falaleev, M. V. Fokin and many others. And abroad – by
R. E. Showalter, A. Favini, A. Yagi and many others. At the department
under the leadership of Sviridyuk the Scientific School was formed. Its main purpose is to
study in different aspects Sobolev type equations and the development of their
applications. One of the latest achievements of the school – is the creation (in
cooperation with A. L. Shestakov) theory of optimal measuring, in which
model-based Shestakov – Sviridyuk restored dynamically distorted signals. |