Numerical Mathematics

Subject description


  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.

The subject is taught in programs

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.

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