# Numerical Methods

## Subject 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.

## Teaching and learning methods

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

## Expected study results

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.

## Basic sources and literature

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

## Stay up to date

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