## Неделен прегед

• ### Mathematical modelling/ Mathematical modelling

Pri Matematičnem modeliranju študenti (relativno) realne probleme rešujejo s pomočjo matematičnih modelov. Študenti se spoznajo s timskim delom in lahko sami, skupaj s kolegi v ekipi (in ob pomoči učiteljske ekipe) izpeljejo projekt od začetka do konca.

Predmet je razdeljen na tri glavna poglavja:

1. Linearni modeli: sistemi linearnih enačb, posplošeni inverzi matrik
2. Nelinearni modeli: vektorske funkcije vektorske spremenljivke, sistemi nelienarnih enačb, krivulje in ploskve
3. Dinamični modeli: diferencialne enačbe in dinamični sistemi

During the course of Mathematical Modelling the students will be solving (relatively) real life problems with the help of mathematical models. Students will be introduced to team work and will be given the opportunity to carry out a complete relatively complex project from the beginning to the very end  together with their colleagues (and with the help of the teaching team) .

The course consists of three main topics:

1. Linear models: systems of linear equations, generalized inverses of matrices
2. Nonlinear models: vector functions of a vector variable, nonlinear systems, curves and surfaces
3. Dynamic models: differential equations and dynamical systems
• ### 19 февруари - 25 февруари

Lectures: Introduction, a linear matematical model, some basics of linear algebra.

• ### 26 февруари - 3 март

Lectures: Generalized matrix pseudoinverses and their use in solving linear systems, the Moore-Penrose pseudoinverse.
• ### 4 март - 10 март

Lecture: SVD and MP inverse computation, underdetermined systems with many and overdetermined systems with no solutions.

Extra lecture (instead of the next week's one): Vector and matrix norm, PCA, introduction into nonlinear models (see the updated lecture notes) and this pdf.

• ### 11 март - 17 март

No lectures this week.
• ### 18 март - 24 март

Lectures: Vector functions. Derivative/Jacobian matrix. Linear approximation. Tangent method. Newton method. Gauss-Newton method.
• ### 25 март - 31 март

Lecture: Rate of convergence of Newton's method. Newton's optimization. Gradient descent. Broyden's method.

• Podroben opis reševanja 1. naloge iz tedna 5 in 1. naloge iz tedna 6.

• ### 1 април - 7 април

Lectures: Curves - different parametrizations, arc length. (Pages up to 115 in the notes)

• ### 8 април - 14 април

This week

Lectures: Curves - different parametrizations, polar coordinates, arc length, area bounded by the curve, natural parametrization, curvature of parametric curves, plotting plane curves.