Infopaket

Computer algebra

Обов’язкова дисципліна для ОП

First

2021/2022

4 Semester

3

LO 2. Be able to use basic principles and methods of mathematical, complex and functional analysis, linear algebra and number theory, analytical geometry, and differential equations, including partial differential equations, probability theory, mathematical statistics and random processes, numerical methods. LO 5. Be able to develop and use in practice algorithms related to the approximation of functional dependencies, numerical differentiation and integration, solving systems of algebraic, differential and integral equations, solving boundary value problems, finding optimal solutions. LO 11. Be able to apply modern technologies of programming and software development, software implementation of numerical and symbolic algorithms. LO 13. Use specialized software products and software systems of computer mathematics in research.

Distance form

Know: basics of mathematical analysis, algebra and geometry, differential equations, mathematical programming, theory of functions of a complex variable. Be able to calculate derivatives (partial, direction, implicit function), have the concept of integral (volume, surface, curvilinear, improper), investigate the convergence and uniform convergence of series, solve systems of linear algebraic equations with parameters, solve ordinary differential equations and their systems, to master the basic concepts of mathematical field theory. Have basic skills: working with a computer, searching for information on the Internet, using translation systems

Module 1. Basic functions of the MAPLE system. Lectures - 6 years, laboratory - 12 years, independent work - 18 years. Basic data types of the MAPLE system, complex data types. Data analysis and conversion commands. Commands for calculating variables and expressions, substitution, conversion of expressions. Imposing restrictions. Computation commands for basic mathematical analysis problems. Module 2. Advanced features of the MAPLE system. Lectures - 8 years, laboratory - 16 years, independent work - 28 years. Calculation of sums, products, decomposition of functions into Taylor and Laurent series, substitution of variables in expressions. Analytical calculation of solutions of systems of equations, inequalities. Finding solutions of differential equations of their systems, recurrent equations. MAPLE graphics capabilities. Construction of graphs and surfaces. Features of graphics packages. Basic programming tools. Use of special functions.

1. V.S. Vladimirov Uravneniya matematicheskoy fiziki. – M.: Nauka, 1981. 2. S.G. Mihlin Kurs matematicheskoy fiziki. – M.: Nauka, 1968. 3. A.N. Tihonov, A.A. Samarskiy Uravneniya matematicheskoy fiziki. – M.: 4. A.B. Vasilev, N.A. Tihonov Integralnyie uravneniya, M.: Moskovskiy unIversitet, 1989. 5. A.V. Kuzmin Konspekt kursu lektsIy RIvnyannya matematichnoYi fIziki http://195.68.210.50/moodle. 6. G.N. Polozhiy Uravneniya matematicheskoy fiziki M.: Vyisshaya shkola 1964. 7. V.P. Mihaylov Diferentsialnyie uravneniya v chastnyih proizvodnyih M.: Nauka, 1983. 8. O.A. Ladyizhenskaya Kraevyie zadachi matematicheskoy fiziki M.: Nauka, 1973. 9. V.S. Vladimirov Sbornik zadach po uravneniyam matematicheskoy fiziki. M.: Nauka, 1986. 10. B.M. Budak, A.A. Samarskiy, A.N. Tihonov Sbornik zadach po matematicheskoy fizike, M.: Nauka, 1972.

Lectures, independent work, recommended literature processing, homework.

Semester assessment: Maximum number of points that can be obtained by a student: 100 points: 1. Laboratory work 1: PH1.1, PH1.2, PH1.3, PH2.1 - 15 points / 9 points 2. Laboratory work 2: РН1.1, РН1.2, РН1.3. PH2.1 - 15 points / 9 points 3. Laboratory work 3: PH1.1, PH1.2, PH1.3, PH2.1 - 15 points / 9 points 4. Laboratory work 4: PH1.1, PH1.2, PH1.3, PH2.1 - 15 points / 9 points 5. Laboratory work 5: PH1.1, PH1.2, PH1.3, PH2.1 - 15 points / 9 points 6. Modular test 25 points / 15 points Final assessment (in the form of a test):.

Ukrainian