Numerical Mathematics

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.

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

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).