# Numerical Mathematics

## Subject description

Lectures:

1. Introduction to numerical computing (numerical errors and stability of numerical algorithms);
2. Linear algebra: systems of linear equations (direct and iterative methods). Matrix eigenvalues (inverse and QR iteration);
3. Interpolation and approximation (Lagrange and Newton interpolation formulas, least squares method, trigonometric approximation);
4. Numerical integration (Newton-Cotes formulas, Romberg integration, Gauss integration formulas, error estimation and step-size selection, numerical differentiation);
5. Ordinary differential equations (Euler and Runge-Kutta methods,, stability, higher order equations, systems of differential equations, boundary value problems), partial differential equations (finite difference, finite element and spectral methods).

Tutorials: Tutorials will illustrate and/or expand concepts presented in lectures by working through (real life) example problems.

Homeworks: Homeworks are essential part of the course. With homeworks the students will test and upgrade their knowledge.

## Objectives and competences

This course explores the basic methods of numerical mathematics. Successful students be able to solve numerical problems they will encounter in their work.

## Teaching and learning methods

Type (examination, oral, coursework, project):

Continuing (homework, midterm exams, project work)

Final (written and oral exam)

Grading: 6-10 pass, 5 fail (according to the rules of University of Ljubljana).

## Expected study results

After successfully completing the course, the students will be able to:

understand and use basic numerical methods,

– know and understand their advantages and weaknesses,

– use appropriate numerical methods for problem solving,

– discover that computer simulations are a necessary ingredient of research work (besides experiments and theory),

– transfer systematic approach to numerical problem solving to other problems.

## Basic sources and literature

B. Orel: Osnove numerične matematike, Založba FE in FRI, Ljubljana, 1997.

D. R. Kincaid, E. W. Cheney: Numerical Analysis, Mathematics of Scientific Computing, 3rd edition, Brooks/Cole, Pacific Grove, 2002.

K. Atkinson, W. Han: Elementary Numerical Analysis, 3rd edition, John Wiley & Sons, Inc., New Jersey, 2003.

L. N. Trefethen, D. Bau: Numerical Linear Algebra, SIAM, Philadelphia, 1997.

R. L. Burden, J. D. Faires, A. M. Burden: Numerical Analysis, 10th edition, Cengage Learning, Boston, 2016.

G. H. Golub, C. F. Van Loan: Matrix Computations, 3rd edition, Johns Hopkins Univ. Press, Baltimore, 1996.

## Stay up to date

University of Ljubljana, Faculty of Electrical Engineering Tržaška cesta 25, 1000 Ljubljana