Weekly outline

  • Mathematical modeling/ Mathematical modeling


  • 18 February - 24 February

    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)

    • 25 February - 3 March

      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)

      Polynomial interpolation

      Basic facts about matrix pseudoinverses

      An introduction to the Moore-Penrose pseudoinverse

      • 4 March - 10 March

        Lecture, Week 3: 

        SVD and PCA, MP inverse and systems with no or many solutions.

        • 11 March - 17 March

          Nonlinear mathematical models, functions from Rto Rm

          Linear approximation.

          Solving systems on nonlinear equations: Newton's method for systems of order n × n, application to local extrema, Gauss-Newton method.

          • 18 March - 24 March

            Parametric curves

            • 25 March - 31 March

              Plane curves

              • 1 April - 7 April

                Curves in polar coordinates
                Parametric surfaces
                • 8 April - 14 April

                  Differential equations: 

                  Degree 1 equations: general and particular solutions, separable, linear equations, directional field

                  • 15 April - 21 April

                    Diferential equations

                    degree 1 equations: homogeneous, exact, existence of solutions

                    numerical methods: Euler, Runge-Kutta


                    • 22 April - 28 April

                      No lectures

                      • 6 May - 12 May

                        Systems of differential equations: 

                        numerical methods (Euler, Runge-Kutta)

                        linear systems


                        • 13 May - 19 May

                          Systems of linear differential equations


                          • 20 May - 26 May

                            Linear autonomous systems of order 2: phase portrait, classification

                            DEs of higher order: connection to systems of DEs, initial and boundary conditions

                            Homogeneous linear higher order DEs 

                            Nonhomogeneous LDEs of order 2 and more, examples: oscillating systems

                            • 27 May - 2 June

                              Nonlinear systems: qualitative behaviour of solutions, phase portrait, limit sets