Faculties and Institutes

The Faculty of Mathematics and Informatics

The Department of Mathematical Analysis

Nickolay D. KOPACHEVSKY, Honored Worker of Science and Technology of Ukraine, Professor, Honored Worker of Public Education of Crimea, Member of Ukrainian National Council on Theoretical and Applied Mechanics, Full Member of Crimean Academy of Sciences and Petrov’s Academy of Science and Art (Sankt-Petersburg, Russia), Head of the International conference KROMSH, Doctor of Physical and Mathematical Sciences, Professor.

E-mail: kopachevsky@tnu.crimea.ua, kopachevsky@list.ru

Web-site: http://nikolay-d-kopachevsky.com, http://kromsh.info

History

It is the oldest department at the University, established in 1963. In different times it was directed by the astronomer and physicist E.F. Skvortsov, Associate Professors B.A. Manson, Sh.Sh. Sutyusheva and V.D. Andronov. Since 1981 it is directed by prof. N.D. Kopachevsky.

Scientific Work

Extensive theoretical and applied scientific researches are carried out by members of math analysis department. The staff-members are engaged in research of modern problems of the mathematical and functional analysis, spectral theory of operators, boundary value problems of math physics, operator *-algebras and algebras of measurable operators, dominant ergodicity theorem, queuing theory. Results of researches are reflected in numerous articles and monographs (see publications in original languages).

The main direction of N.D. Kopachevsky’s scientific school works is application of methods of the theory of linear operators to problems of mechanics of continuous environments. In particular, it is studying of the differential and integral-differential equations in Hilbert space that arise in researches of wave and small movements’ processes in the confined reservoirs. A qualitative investigation of spectral properties of differential operators, the theory of operator sub matrixes with unlimited operator factors, spectral transmission problems in Lipshitz domains, solvability of boundary value problems of math physics are also considered.

Five PhD- dissertations and two math doctor's degree have been defended since 2005. Three PhD- dissertations are ready to defending (status of autumn 2010).

More than 5 scientific and students seminars work at the department. During 21 years the department organizes the International Crimean Autumn Mathematical School-symposium on Spectral and Evolution Problems at the Batiliman Bay near Sevastopol. In 2005 more than 220 scientists from 14 countries of the world took part in its work, among them more than 80 doctors of sciences and 9 full members and member-correspondents of national Academies of Sciences of Ukraine, Russia, Poland, Armenia and Georgia. Works of School-symposium are issued annually in publishing house of TNU as scientific journal “Spectral and Evolution Problems”.

Beside individual scientific activity, the collective of the department since 2006 conducts work on following scientific subjects: "Mathematical Analysis and Its Applications", the leader – prof. N.D. Kopachevsky, "Development of Operational Methods in Linear and Nonlinear Analysis, Initial Boundary value, Spectral, Variation and Bifurcation Problems of Math Physics", the leader – prof. N.D. Kopachevsky.

Faculty Members

Nickolay D. Kopachevskiy, the Head of the Department, Doctor of Physical and Mathematical Sciences, Professor.

Courses Taught:

• Applied Functional Analysis;
• Operator Methods of Mathematical Physics;
• Operator Methods of Hydromechanics;
• Special Course “Spectral Theory of Operator Pencils and its Applications”;
• Special Course “Calculus of Variations and Its Applications”;
• Special Course “Differential Equations in Banach Spaces and Their Applications”;
• Special Course  “Operator Methods in Mathematical Physics”;
• Special Course “Operator Methods in Linear Hydrodynamics”;
• Special Course “Volterra Integral-Differential Equation in Banach Space”;
• Scientific Seminars “Operator Methods in Mechanics of continuous environments”, “Linear Operators Theory”.

Mustafa A. Muratov, Doctor of Physical and Mathematical Sciences, Professor.

Courses Taught:

• Mathematical Analysis;
• Theory of Complex Variable Functions;
• Operational Calculus;
• Mathematics for Economists;
• Special Course “Elements of Spectral Theory of Linear Operators in Hilbert Spaces”;
• Special Course “Finite-dimensional von Neumann Algebras”;
• Special Course “Finite-dimensional Linear Analysis”;
• Special Course “Ergodic Theorems in the Permutable Invariant Spaces”.
• Scientific Seminars “Algebras of Measurable Operators”, “Symmetric Spaces of Measurable Functions”.

Alexander I. Kovalenko, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis;
• Additional Chapters of Mathematical Analysis;
• Probability Theory and Mathematical Statistics;
• Queuing theory;
• Special Course “Elements of the Mathematical Theory of Reliability”.

Boris D. Marianin, PhD, Associate Professor.

Courses Taught:

• Higher Mathematics;
• Bases of Higher Mathematics;
• Probability Theory and Mathematical Statistics;
• Random Processes;
• Special Course “Differential Forms”;
• Special Course “Differential Calculus in Infinite-dimensional Spaces”;
• Special Course “Elements of Random Processes Theory”.

Alexey S. Tikhonov, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis and Additional Chapters of Mathematical Analysis;
• Probability Theory and Mathematical Statistics;
• Theory of Complex Variable Functions;
• Special Course “Selected Issues of Elementary and Higher Mathematics”;
• Special Course “Selected Issues of the Group Theory”;
• Special Course “Riemann Surfaces”.

Vladimir P. Smolich, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis;
• Theory of Complex Variable Functions;
• Probability Theory and Mathematical Statistics;
• Queuing theory;
• Special Course “Linear Operators Theory”;
• Special Course “Linear Operators in Hilbert Space”;
• Special Course “Operational Calculus”.

Svetlana I. Smirnova, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis;
• Probability Theory and Mathematical Statistics.

Yulia S. Pashkova, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis;
• Probability Theory and Mathematical Statistics;
• Complex Analysis;
• Operational Calculus;
• Special Course “Elements of Spectral Theory of Linear Operators in the Hilbert Spases”;
• Special Course “Ergodic Theorems in the Permutable Invariant Spaces”;
• Special Course “Symmetric Spaces of Measurable Functions”.

Dmitriy A. Zakora, PhD, Associate Professor.

Courses Taught:

• Operator Methods in Mathematical Physics;
• Mathematical Analysis;
• Differential Equation in Banach Space;
• Operational Methods of Hydromechanics;
• Probability Theory and Mathematical Statistics;
• Additional Chapters of Mathematical Analysis;
• Special Course “Differential Equation in Banach Space and Their Applications”.

Pavel A. Starkov, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis;
• Probability Theory and Mathematical Statistics;
• Computer Theories in Mathematics;
• Selected problems of Mathematical Analysis;
• Series Theory;
• Special Course “Introduction to Asymptotic Methods”.

Denis O. Tsvetkov, PhD, Associate Professor.

Courses Taught:

• Mathematical Analysis;
• Probability Theory and Mathematical Statistics;
• Complex Analysis;
• Theory of Complex Variable Functions;
• Random Processes.

Victor I. Voititskiy, PhD, Assistant.

Courses Taught:

• Mathematical Analysis;
• Probability Theory and Mathematical Statistics;
• Special Course “Abstract Green’s Formula”;
• Special Course “Spectral Theory of Operator’s Pencils”.

Lidia V.Koreneva, Senior Lecturer.

Courses Taught:

• Mathematical Analysis (practice);
• Higher Mathematics (practice);
• Special Course “Problem Tasks of Elementary Mathematics”.

Galina I.Kushnereva, Senior Lecturer.

Courses Taught:

• Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (practice);
• Theory of Complex Variable Functions (practice);
• Higher Mathematics (practice).

Boris M.Vronskiy, Senior Lecturer.

Courses Taught:

• Mathematical Analysis (practice);
• Additional Chapters of Mathematical Analysis (practice);
• Probability Theory and Mathematical Statistics (practice);
• Theory of Complex Variable Functions (practice);
• Complex Analysis (practice);
• Higher Mathematics (practice).