The aim of studying and bibliography

The main aim of study:

The general information about the module:

Bibliography required to complete the module

Bibliography used during classes/laboratories/others

1	Калиткин Н.Н.	Численные методы.	М.:Наука.	1978
2	Ортега Дж., Пул У.	Введение в численные методы решения дифференциальных уравнений.	М.:Наука.	1986.
3	Mikłaszewska N.E., Mikłaszewski R.I.	Słownik matematyczny polsko-rosyjski	M.:Fizmatgiz.	1963

Bibliography to self-study

1

Самарский А.А., Гулин А.В.

Численные методы

М.:Наука.

1989

Basic requirements in category knowledge/skills/social competences

Formal requirements: The student satisfies the formal requirements set out in the study regulations

Basic requirements in category knowledge: K_W02, K_W04, K_W13

Basic requirements in category skills: K_U02, K_U03, K_U04,K_U13, K_U14, K_U15,K_U16, K_U17

Basic requirements in category social competences: K_K02, K_K04, K_K06, K_K07

Module outcomes

MEK	The student who completed the module	Types of classes / teaching methods leading to achieving a given outcome of teaching	Methods of verifying every mentioned outcome of teaching	Relationships with KEK	Relationships with PRK
01				K_W02+ K_W04+ K_W13+++ K_U02+++ K_U03+ K_U04+ K_U13+ K_U14+ K_U15+ K_U16+ K_U17++ K_K01+ K_K02++ K_K04+ K_K06++ K_K07+	P7S_KK P7S_KO P7S_KR P7S_UK P7S_UO P7S_UU P7S_UW P7S_WG P7S_WK

Attention: Depending on the epidemic situation, verification of the achieved learning outcomes specified in the study program, in particular credits and examinations at the end of specific classes, can be implemented remotely (real-time meetings).

The syllabus of the module

Sem.	TK	The content	realized in	MEK
2	TK01	Mathematical models and numerical methods. Direct methods for solving systems of linear equations. Gaussian elimination. Calculating the determinant and matrix inversion. Iterative methods for solving systems of linear equations.	C01-C03	MEK01
2	TK02	Numerical solution of nonlinear equations and their systems	C04-C06	MEK01
2	TK03	Approximation of function. Lagrange's and Newton's interpolation polynomials. Estimation of error for interpolation polynomial. The method of least squares for approximation functions. Numerical differentiation.	C07-C10	MEK01
2	TK04	Numerical integration. Newton and Cotes quadrature. Composite Newton and Cotes quadrature.	C11-C13	MEK01
2	TK05	Methods of numerical solution of the initial value problem for ordinary differential equations	C14-C15	MEK01

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Class (sem. 2)	The preparation for a Class: 15.00 hours/sem.	contact hours: 30.00 hours/sem.
Advice (sem. 2)	The preparation for Advice: 2.00 hours/sem.	The participation in Advice: 1.00 hours/sem.
Credit (sem. 2)	The preparation for a Credit: 5.00 hours/sem.	The oral credit: 2.00 hours/sem.

The way of giving the component module grades and the final grade

The type of classes	The way of giving the final grade
Class	Written work (tasks). Working in the classroom
The final grade	Average rating: written work(70%), work in the classroom (30%)

Sample problems

Required during the exam/when receiving the credit
kolok3.pdf

Realized during classes/laboratories/projects
Zad2.pdf

Others
(-)

Can a student use any teaching aids during the exam/when receiving the credit : no

The contents of the module are associated with the research profile: yes

1	B. Datsko; M. Kutniv	Explicit numerical methods for solving singular initial value problems for systems of second-order nonlinear ODEs	2024
2	N. Khomenko; A. Kunynets; M. Kutniv	Algorithmic Realization of an Exact Three-Point Difference Scheme for the Sturm–Liouville Problem	2023
3	N. Khomenko; A. Kunynets; M. Kutniv	Three-Point Difference Schemes of High Order of Accuracy for the Sturm–Liouville Problem	2023
4	B. Datsko; V. Gafiychuk; C. Naconechna	Pattern Formation in Activator-Inhibitor Fractional Reaction-Diffusion Systems	2022
5	M. Król; M. Kutniv	New Algorithmic Implementation of Exact Three-Point Difference Schemes for Systems of Nonlinear Ordinary Differential Equations of the Second Order	2022
6	B. Datsko	Mathematical modeling of complex spatio‐temporal dynamics in autocatalytic reaction‐diffusion systems with anomalous diffusion	2021
7	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	New explicit high‐order one‐step methods for singular initial value problems	2021
8	G. Harmatiy; B. Kalynyak; M. Kutniv	Uncoupled Quasistatic Problem of Thermoelasticity for a Two-Layer Hollow Thermally Sensitive Cylinder Under the Conditions of Convective Heat Exchange	2021
9	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	A new approach to constructing of explicit one-step methods of high order for singular initial value problems for nonlinear ordinary differential equations	2020
10	B. Datsko; M. Kutniv; A. Włoch	Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion	2020
11	B. Datsko; I. Podlubny; Y. Povstenko	Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact	2019