Mathematical Modelling

Weekly outline

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  Mathematical modeling/ Mathematical modeling

  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

  • Course rules (in Slovene) / about the course Page

    
    

  • Forumi

  • Novice / news Forum
  • Pomoč in vprašanja / Q and A Forum
  • Gradiva/Lecture notes

  • MM lecture notes 2021/22 File Uploaded 12/02/23, 20:31
  • Viri/Literature Page
  • Stari izpiti/Exams from previous years Page
  • Časovnica Page
  • Programi za numerično računanje Page
  • Uvod v octave Page
  • Testiranje programov Page
  • Plonk listek za LaTeX/LaTeX cheatsheet URL
  • Programerski triki v octave File
  • Domače naloge / Home assignments

  • Kakšna je dobra rešitev naloge Page
  • 1st home assignment File Uploaded 7/03/23, 19:59
  • Oddaja 1. domače naloge/ 1st homework submission Assignment
  • 2. domača naloga File Uploaded 28/03/23, 20:53
  • 2nd home assignment (in English) File Uploaded 28/03/23, 20:54
  • Oddaja 2. domače naloge / 2nd home assignment submission
  • 3. domača naloga File Uploaded 19/04/23, 17:08
  • 3rd home assignment File Uploaded 19/04/23, 17:10
  • Oddaja 3. domače naloge / 3rd home assignment submission
  • Projektna naloga / Project assignment

  • Teme za projekte / Project topics Page
  • Exams

    1. exam: June 7th, (Wed)
    2. exam: June 23rd, (Thur) 
    3. exam: September 5th, (Tue)
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  14 February - 20 February

  Lectures: Introduction, a linear matematical model, some basics of linear algebra (solving a linear system of equations, a characterization of the inverse of a square matrix).

  • Lecture notes: chapters 0 and 1 File Uploaded 13/02/23, 15:19
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  21 February - 27 February

  Lectures: Generalized matrix pseudoinverses and their use in solving linear systems, the Moore-Penrose pseudoinverse, introduction to a singular value decomposition.

  • Naloge za vaje, 2. teden File Uploaded 19/02/23, 20:46
  • oddajniki.txt File
  • razdalje.txt File
  • Rešitve nalog, 1. teden Page
  • sprejemnik.m File
  • Problem sessions exercises, week 2 File Uploaded 19/02/23, 20:47
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  28 February - 6 March

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

  • Naloge za vaje, 3. teden File Uploaded 26/02/23, 21:25
  • Rešitve nalog, 3. teden Page
  • projekcija.m File Uploaded 29/03/17, 12:34
  • Problem sessions exercises, week 3 File Uploaded 26/02/23, 21:26
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  7 March - 13 March

  Lectures: PCA. Nonlinear mathematical models, Tangent method, Newton's method for square systems (introduction).

  • Lectures: chapters 0-2 File Uploaded 7/03/23, 07:47
  • Naloge za vaje, 4. teden File
  • Problem sessions exercises, week 4 File Uploaded 5/03/23, 20:50
  • lena512.mat File
  • Rešitve 1. naloge, 4. teden Page
  • Rešitev 2. naloge, 4. teden Page
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  14 March - 20 March

  Lectures: Newton's optimization, Gradient descent. Broyden's method, Gauss-Newton method.

  • Naloge za vaje, 5. teden File
  • Problem sessions exercises, week 5 File Uploaded 12/03/23, 08:07
  • newton.m File
  • krivulja.m File Modified 17/03/20, 16:38
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  21 March - 27 March

  Lectures: Curves - different parametrizations, polar coordinates, arc length, area bounded by the curve, natural parametrization.

  • Lectures: chapters 0-3 File Uploaded 13/03/23, 21:02
  • Naloge za vaje, 6. teden File
  • Problem sessions exercises, week 6 File Uploaded 19/03/23, 18:42
  • Podatki za 1. nalogo / Data for 1st exercise Page
  • Uporaba izpeljav 1. naloge v Octave / Use of derivations for the 1st exercise in Octave Page
  • sprejemnik.m File
  • Reševanje nelinearnih enačb File Uploaded 26/03/18, 14:55

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

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  28 March - 3 April

  Lectures: Numerical integration, curvature of parametric curves, plotting plane curves, surfaces (introduction).

  • Naloge za vaje, 7. teden File
  • Problem sessions exercises, week 7 File Uploaded 26/03/23, 12:47
  • gradmet.m File
  • razdaljaK.m File Uploaded 17/04/20, 09:46
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  4 April - 10 April

  Lectures: Parametrization of surfaces. Surface of revolution. Tangent plane. Differential equations: introduction.

  • Lectures: chapters 0-4 File Uploaded 3/04/23, 23:04
  • Naloge za vaje, 8. teden File
  • Problem sessions exercises, week 8 File Uploaded 2/04/23, 20:52
  • presecisce.m File
  • presecisca.m File
  • presekKrivulj.m File Uploaded 15/04/18, 13:22
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  11 April - 17 April

  Lectures: Differential equations - Applications, separation of variables, first order linear ODE, variation of constants, orthogonal trajectories.

  • Naloge za vaje, 9. teden File
  • Problem sessions exercises, week 9 File Uploaded 11/04/23, 05:21
  • ploscina.m File
  • obseg.m File
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  18 April - 24 April

  Lectures: Homogeneous DE, exact DE, direction field, Euler's method, Runge-Kutta methods. 

  • Naloge za vaje, 10. teden File Uploaded 16/04/23, 17:20
  • Problem sessions exercises, week 10 File Uploaded 16/04/23, 17:21
  • euler.m File
  • rk4.m File
• 

  25 April - 1 May

  Lectures: DOPRI5. Transforming an ODE of higher order into a system of first order ODE. Systems of differential equations. Autonomous linear systems. Numerical methods for systems.

  • Naloge za vaje, 11. teden File Uploaded 24/04/23, 10:15
  • Problem sessions exercises, week 11 File Uploaded 24/04/23, 10:16
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  2 May - 8 May

  Not available
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  9 May - 15 May

  Lectures: Phase portraits, linearization of a nonlinear system, autonomous linear DE of higher order.

  
  

  • Naloge za vaje, 13. teden File Uploaded 8/05/23, 06:02
  • Problem sessions exercises, week 13 File Uploaded 8/05/23, 06:02
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  16 May - 22 May

  Lectures: Wronskian determinant, nonhomogeneous second order DEs.

  • Naloge za vaje, 14. teden File Uploaded 14/05/23, 22:15
  • Problem sessions exercises, week 14 File Uploaded 14/05/23, 22:15
  • izstrelek.m File
  • dnewton.m File
  • broyden.m File
  • secant.m File
  • Primer reševanja naloge (14. teden) / Solution example (week 14) Page
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  23 May - 29 May

  Lectures: Preparations for the exams.

  • Naloge za vaje, 15. teden File Uploaded 21/05/23, 21:00
  • Problem sessions exercises, week 15 File Uploaded 21/05/23, 21:00