# Numerical Methods

## Course description

Solving nonlinear equations (bisection method, secant method, Newton method). Systems of linear equations (Gaussian elimination, iterative methods, boundary value problems, overdetermined and underdetermined systems of linear equations). Interpolation and approximation (polynomial interpolation, cubic splines, least squares method). Numerical integration (trapezoidal rule, Simpson rule, Romberg method, singular integrals). Ordinary differential equations (Euler method, Heun method, shooting method). Partial differential equations (finite difference method).

## Objectives and competences

Understanding of basic numerical methods, their meaning and usage. Develop numerical-analytical thinking. To get to know programming tools Matlab and Octave.

## Learning and teaching methods

Lectures and laboratory tutorials. Homework assignements in Matlab or Octave.

## Intended learning outcomes

After successful completion of the course, students should be able to:

• describe basic numerical methods,
• numerically solve nonlinear equations, systems of linear equations and problems with approximation and interpolation,
• numerically compute definite integrals and numerically solve ordinary and partial differential equations,
• use the programming tools Matlab and Octave for solving numerical problems,
• critically analyse and numerically interpret technical problems that we encounter in practise,
• critically evaluate the solution.

## Reference nosilca

1. OMLADIČ, Matjaž, STOPAR, Nik. Final solution to the problem of relating a true copula to an imprecise copula. Fuzzy sets and systems : international journal of soft computing and intelligence. Aug. 2020, vol. 393, str. 96-112. ISSN 0165-0114.

2. OMLADIČ, Matjaž, STOPAR, Nik. A full scale Sklar's theorem in the imprecise setting. Fuzzy sets and systems : international journal of soft computing and intelligence. Aug. 2020, vol. 393, str. 113-125. ISSN 0165-0114.

3. STOPAR, Nik. Rank of elements of general rings in connection with unit-regularity. Journal of Pure and Applied Algebra. Apr. 2020, vol. 224, iss. 4, art. 106211 (11 str.). ISSN 0022-4049.

4. ĐURIĆ, Alen, JEVĐENIĆ, Sara, STOPAR, Nik. Compressed zero-divisor graphs of matrix rings over finite fields. Linear and Multilinear Algebra. 2021, vol. 69, iss. 11, str. 2012-2039. ISSN 0308-1087.

5. DOLINAR, Gregor, KUZMA, Bojan, STOPAR, Nik. Characterization of orthomaps on the Cayley plane. Aequationes mathematicae. April 2018, vol. 92, iss. 2, str. 243-265. ISSN 0001-9054.

## Study materials

1. N. Stopar: Numerične metode, zapiski predavanj, https://e.fe.uni-lj.si, 2021.
2. B. Plestenjak: Razširjen uvod v numerične metode, DMFA-založništvo, 2015.
3. R.Burden, J.D.Faires: Numerical Analysis, 9th ed., Brooks/Cole, Boston 2010.
4. Jurčič Zlobec Borut, Perne Andrej: Octave z uvodom v numerične metode, Založba FE, 2009.
5. B. Orel: Osnove numerične matematike, Založba FE in FRI, Ljubljana, 2004.
6. B. Jurčič-Zlobec, A. Berkopec: Matlab z uvodom v numerične metode, Založba FE in FRI, Ljubljana, 2005.
7. Spletna učilnica eFE https://e.fe.uni-lj.si

## Bodi na tekočem

Univerza v Ljubljani, Fakulteta za elektrotehniko, Tržaška cesta 25, 1000 Ljubljana