Basics of calculation methods
Course: Applied Mathematics
Structural unit: Faculty of Computer Science and Cybernetics
Title
Basics of calculation methods
Code
ННД.19
Module type
Обов’язкова дисципліна для ОП
Educational cycle
First
Year of study when the component is delivered
2022/2023
Semester/trimester when the component is delivered
5 Semester
Number of ECTS credits allocated
4
Learning outcomes
LO 5. Be able to develop and use in practice algorithms related to approximation of functional dependencies, numerical differentiation and integration, solution of systems of algebraic, differential and integral equations, solution of boundary value problems, search for optimal solutions.
LO 18. Communicate effectively about information, ideas, problems and solutions with specialists and society in general.
Form of study
Full-time form
Prerequisites and co-requisites
To successfully study the discipline "Fundamentals of calculation methods", a student must meet the following requirements:
Successful completion of courses
1. Mathematical analysis.
2. Algebra and geometry
3. Programming
4. Differential equations
5. Object-oriented programming
Knowledge:
1. Basic definitions and theorems of mathematical analysis, algebra and geometry, research of operations, theory of differential equations.
2. Procedural and object-oriented programming.
Skill:
1. Solve problems of mathematical analysis, algebra and geometry, operations research, theory of differential equations.
2. Program in procedural and object-oriented styles.
Course content
1 Topic 1. Problems of the theory of calculation methods and the technology of the computational experiment method. Elements of the theory of errors.
2 Topic 2. Methods of solving nonlinear equations.
3 Topic 3. Direct and iterative methods of solving systems of linear algebraic equations. Conditionality of systems of linear algebraic equations. Methods of solving systems of nonlinear equations.
4 Topic 4. The complete and partial problem of solving eigenvalue problems
Control work No. 1
5 Topic 5. Interpolation problem. Interpolation formulas and evaluation of residual terms. Interpolation with multiple nodes.
6 Topic 6. Spline interpolation. The problem of inverse interpolation. Numerical differentiation problem.
Control work No. 2
Recommended or required reading and other learning resources/tools
1. Sharyi S.P. Kurs vychislitel-nykh metodov. 2018.
2. M.M.Moskal-kov, A.І.Rizhenko, S.O.Voitsekhovs-kii ta іn. Praktikum z
metodіv obchislen-. Kiїv. MAUP. 2006.
3. M.M.Moskal-kov, A.І.Rizhenko, S.O.Voitsekhovs-kii ta іn. Praktikum z
metodіv obchislen-. Kiїv. MAUP. 2008.
4. Bakhvalov N.S., Zhidkov N.P., Kobel-kov G.N. Chislennye metody.
BINOM, 2011.
5. Makarov V.L., Gavriliuk I.P. Metodi obchislen-. Kiїv, Vishcha shkola, 1995.
6. Kalitkin, N.N. Chislennye metody. - BHV, 2014.
7. Volkov A.F. Chislennye metody. – Lan-, 2008.
..
Planned learning activities and teaching methods
Lectures, laboratory classes, independent work
Assessment methods and criteria
Semester assessment:
1. Control paper No. 1: PH 1.1, PH 1.2 – 15/9 points.
2. Control work No. 2: PH 1.3 – 15/9 points.
3. Laboratory work No. 1: RN 1.1, RN 2.1, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 15/9 points.
4. Laboratory works No. 2,3: RN 1.2, RN 2.2, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 15/9 points.
5. Laboratory work No. 4: RN 1.3, RN 2.3, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 15/9 points.
6. Assessment of independent work: PH 1.1, PH 1.2, PH 1.3, PH2.1, PH 2.2, PH 2.3, PH 4.1, PH 4.2 - 10/6 points.
Final evaluation: credit
Language of instruction
Ukrainian
Lecturers
This discipline is taught by the following teachers
Departments
The following departments are involved in teaching the above discipline