The aim of studying and bibliography

The main aim of study: The aim of the course is to introduce students with the basic numerical methods.

The general information about the module: The module contains the content of methods of solving linear and nonlinear systems equations, interpolation, numerical integration, solving the initial value problems for ordinary differential equations.

Bibliography required to complete the module

Bibliography used during lectures

1	G. Dahlquist, A. Bjorck	Metody numeryczne	PWN, Warszawa.	1987
2	Z. Fortuna, B. Macukow, J. Wasowski	Metody numeryczne	WNT, Warszawa.	1998

Bibliography to self-study

1

J. i M. Jankowscy

Przegląd metod i algorytmów numerycznych

WNT, Warszawa.

1988

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: Basic knowledge of mathematical analysis and matrix calculations.

Basic requirements in category skills: Ability to solve simple tasks of of mathematical analysis, the ability to perform calculations on arrays, the ability to use the calculator and computer.

Basic requirements in category social competences: It can appropriately determine the priorities for the realization of one's own or other tasks

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	Knows the basic numerical methods for solving equations and systems of linear equations.	lectures, employments practical		K_W03+ K_W08+++ K_U11+ K_K01+	P6S_KK P6S_UO P6S_UU P6S_UW P6S_WG P6S_WK
02	Student knows the basic methods of numerical integration, and numerical solution of differential equations.	lectures, employments practical		K_W04+ K_W08++ K_U15+ K_K01+	P6S_KK P6S_UW P6S_WG P6S_WK
03	Can to solve numerically a simple problem, using the computational tools.	employments practical		K_W08+ K_K01+	P6S_KK P6S_WG

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
5	TK01	Mathematical modeling and numerical calculations. Write numbers in the computer. Classification of calculation errors.	W01, C01	MEK01
5	TK02	Direct methods for solving systems of linear equations. The method of Gaussian elimination. Calculations determinants and inverse matrices. Elimination method for systems with tridiagonal matrix. Iterative methods. The methods of successive approximations (simple iteration), Jacobi, Gauss-Seidel.	W02, W03, C02, C03	MEK01 MEK03
5	TK03	Methods for solving nonlinear equations. Methods bisection, successive approximations (simple iteration), Newton’s, secant. Methods for solving systems of nonlinear equations. The method of successive approximations, Newton’s.	W04, C04	MEK01 MEK03
5	TK04	Function approximation. Interpolation polynomials of Lagrange and Newton. Estimation of the error of the interpolation polynomial. The method of least squares. Numerical differentiation..	W05, C05	MEK01 MEK03
5	TK05	Numerical integration. Newton-Cotes quadrature. Formulas of rectangles, trapezoids, Simpson. Composite quadrature formulas.	W06, C06	MEK02 MEK03
5	TK06	Methods of numerical solution of the initial value problem for ordinary differential equations. Taylor series and Runge-Kutta methods. Linear multistep methods. Order of approximation and stability of linear multistep methods	W07, W08, C07, C08	MEK02 MEK03

The student's effort

The type of classes	The work before classes	The participation in classes	The work after classes
Lecture (sem. 5)		contact hours: 15.00 hours/sem.	complementing/reading through notes: 3.00 hours/sem. Studying the recommended bibliography: 3.00 hours/sem.
Class (sem. 5)	The preparation for a Class: 5.00 hours/sem. The preparation for a test: 5.00 hours/sem.	contact hours: 15.00 hours/sem.	Finishing/Studying tasks: 5.00 hours/sem.
Advice (sem. 5)	The preparation for Advice: 1.00 hours/sem.	The participation in Advice: 1.00 hours/sem.
Credit (sem. 5)	The preparation for a Credit: 5.00 hours/sem.	The written 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
Lecture	Written work (tasks).
Class	Work in the classroom.
The final grade	Average rating: written work, class work.

Sample problems

Required during the exam/when receiving the credit
kolok1.pdf

Realized during classes/laboratories/projects
Zad1.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	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
5	B. Datsko; A. Kunynets; M. Kutniv; A. Włoch	New explicit high‐order one‐step methods for singular initial value problems	2021
6	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
7	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
8	B. Datsko; M. Kutniv; A. Włoch	Mathematical modelling of pattern formation in activator–inhibitor reaction–diffusion systems with anomalous diffusion	2020