Mathematical modeling/ Mathematical modeling
- 2. izpit iz Matematičnega modeliranja / 2nd Mathematical modelling exam Assignment
1. teden predavanj: Uvod (Introduction), linearni matematični modeli (linear mathematical models), ponovitev linearne algebre: reševanje sistemov linearnih enačb (repetition from linear algebra: solving systes of linear equations), posplošeni matrični inverzi (matrix pseudoinverses)
2. teden predavanj (2nd week of classes): Posplošeni matrični inverzi (matrix pseudoinverse), Moore-Penroseov inverz (Moore-Penrose pseudoinverse), ponovitev SVD razcepa (singular value decomposition), sistemi z neskončno mnogo rešitvami (systems with infinitely many solutions)
Lecture, Week 3:
SVD and PCA, MP inverse and systems with no or many solutions.
Nonlinear mathematical models, functions from Rn to Rm
Solving systems on nonlinear equations: Newton's method for systems of order n × n, application to local extrema, Gauss-Newton method.
Curvature of parametric curves, plane curves, curves in polar coordinates, applications
Differential equations. General and particular solutions, separable DEs, first order linear DEs, examples.
Differential equations: homogeneous, exact, existence of solutions, numerical method for solving - Euler, Runge-Kutta
Systems of differential equations: autonomous systems of linear 1st order systems, tranfsormation of higher orders ODEs to systems of DEs, general autonomous systems, numerical methods (Euler, Runge-Kutta).
Systems of differential equations:
phase portraits of autonomous 2x2 systems, classification of equillibrium points, nonhomgeneous systems
Differential equations of order 2 or more
Nonhomogeneous LDEs, vibrations