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Fundamentals of calculation methods

Обов’язкова дисципліна для ОП

First

2023/2024

5 Semester

4

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 18. Communicate effectively on information, ideas, problems and solutions with professionals and society.

Distance form

To successfully learn the discipline "Fundamentals of Computational Methods" the student should satisfy the following requirements: know: (a) the basic definitions and theorems of mathematical analysis, algebra and geometry, operations research, theory of differential equations; (b) procedural and object-oriented programming. be able: (a) to solve problems of mathematical analysis, algebra and geometry, the theory of differential equations by classical methods; (b) to program in procedural and object-oriented styles.

Block 1. Approximate methods for solving equations and systems of equations. Elements of error theory. Approximate methods for solving nonlinear equations. Direct and iterative methods for solving systems of linear algebraic equations. Methods for solving systems of nonlinear equations. Complete and partial problem of solving problems on their own values. Block 2. Interpolation approximation of functions and its application. Interpolation problem. Interpolation formulas and estimation of residual terms. Interpolation with multiple nodes. Spline interpolation. The problem of inverse interpolations. Numerical differentiation.

Sharyiy S.P. Kurs vyichislitelnyih metodov. 2018. M.M.Moskalkov, A.I.Rizhenko, S.O.Voytsehovskiy ta In. Praktikum z metodIv obchislen. KiYiv. MAUP. 2006. M.M.Moskalkov, A.I.Rizhenko, S.O.Voytsehovskiy ta In. Praktikum z metodIv obchislen. Nablizhennya funktsIy. KiYiv. MAUP. 2008. BurkIvska V.L., VoytsehIvskiy S.O., Rizhenko A.I. ta In. Metodi obchislen. KiYiv, Vischa shk. 1998. Bahvalov N.S., Zhidkov N.P., Kobelkov G.N. Chislennyie metodyi. BINOM, 2011. Makarov V.L., Gavrilyuk I.P. Metodi obchislen. KiYiv, Vischa shkola, 1995. Kalitkin, N.N. Chislennyie metodyi. - BHV, 2014. Volkov A.F. Chislennyie metodyi. – Lan, 2008. Samarskiy, A.A. Vvedenie v chislennyie metodyi. - Lan, 2009. A.V.Gulin, O.S.Mazhorova, V.A.Morozova. Vvedenie v chislennyie metodyi v zadachah i uprazhneniyah. «Argamak-media», 2014. N.S. Bahvalov, A.A Kornev, E.V. Chizhonkov. Chislennyie metodyi. Resheniya zadach i uprazhneniya. Binom, 2016. ...

Lectures, independent work, laboratory works, recommended literature processing, doing homework.

Intermediate assessment: The maximal number of available points is 100. 1. Test work №1: RN 1.1,RN 1.2– 15/9 points. 2. Test work №2: RN 1.3– 15/9 points. 3. Laboratory work № 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 № 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 № 4: RN 1.3, RN 2.3, RN 3.1, RN 3.2, RN 4.1, RN 4.2 – 15/9 points. Assessment of independent work: RN 1.1,RN 1.2,RN 1.3,RN 2.1,RN 2.2, RN 2.3, RN 4.1, RN 4.2 10/6 points. Final assessment: The test is set on the basis of current control as the sum of points for all successfully assessed learning outcomes; poits below the minimum level are not added to the final point.

Ukrainian