Infopaket

Numerical analysis

ННД.20

Обов’язкова дисципліна для ОП

First

2022/2023

7 Semester

4

LO15. To be able to organize one's own activities and obtain a result within a limited time.

Full-time form

To successfully study the discipline "Numerical analysis", 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 6. Basics of calculation methods Knowledge: 1. Basic definitions and theorems of mathematical analysis, algebra and geometry, operations research, theory of differential equations, basics of calculation methods. 2. Procedural and object-oriented programming. Skill: 1. To solve the problems of mathematical analysis, algebra and geometry, operations research, the theory of differential equations, the basics of calculation methods. 2. Program in procedural and object-oriented styles.

1 Topic 1. Approximation of functions. Element of best approximation in linear normalized and Hilbert spaces. 2 Topic 2. Approximation of discrete functions. The method of least squares and its application. 3 Topic 3. Approximate calculation of integrals. Quadrature formulas of the interpolation type. 4 Topic 4. Quadrature formulas of the highest algebraic degree of accuracy. Approximate calculation of improper integrals, integrals of rapidly oscillating functions. 5 Topic 5. Approximate methods of solving the Cauchy problem. Approximate analytical methods. Numerical one-step methods. 6 Topic 6. Multi-step methods of solving the Cauchy problem and methods of their implementation. 7 Topic 7. Numerical methods for solving boundary value problems for systems of ordinary differential equations.

1. M.M.Moskal-kov, A.І.Rizhenko, S.O.Voitsekhovs-kii ta іn. Praktikum z metodіv obchislen-. Kiїv, MAUP. 2008. 2. Sharyi S.P. Kurs vychislitel-nykh metodov. NGU, 2018. 3. Bakhvalov N.S., Zhidkov N.P., Kobel-kov G.N. Chislennye metody. BINOM, 2011. 4. Makarov V.L., Gavriliuk I.P. Metodi obchislen-. Kiїv, Vishcha shkola, 1995. 5. Golubeva K. M., Denisov S. V., Kashpur O. F., Kliushin D. A., Rizhenko A. І. Chisel-nі metodi іntegruvannia. K., 2019. 6. Kalitkin, N.N. Chislennye metody. - BHV, 2014. 7. Volkov A.F. Chislennye metody. – Lan-, 2008. ..

Lectures, laboratory classes, independent work

Semester assessment: 1. Control work #1: PH 1.1, PH 1.2– 10/6 points. 2. Control work #2: PH 1.3, PH 1.4 – 10/6 points. 3. Laboratory work No. 1: RN 1.1, RN 2.1, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 10/6 points. 4. Laboratory work No. 2: RN 1.2, RN 2.2, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 10/6 points. 5. Laboratory work No. 3: RN 1.3, RN 2.3, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 8/5 points. 6. Laboratory work No. 4: RN 1.4, RN 2.4, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 7/4 points. 7. Assessment of independent work: PH 1.1, PH 1.2, PH 1.3, PH 1.4, PH2.1, PH 2.2, PH 2.3, PH 2.4, PH 4.1, PH 4.2 - 5/3 points. Final evaluation (in the form of an exam): 1. The maximum number of points that can be obtained by a student: 40/24 points/(s). 2. Learning outcomes that will be assessed: PH 1.1, PH 1.2, PH 1.3, PH 1.4, PH 2.1, PH 2.2, PH 2.3, PH 2.4. 3. Form of conduct: written work. 4. Types of tasks: 4 written tasks (1 theoretical question and 3 practical tasks). ..

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