Mathematical Modelling

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  Mathematical modelling/ Mathematical modelling

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  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. Krivulje in ploskve
  4. 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 teamwork 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. Curves and surfaces
  4. Dynamic models: differential equations and dynamical systems

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• Select section 17 February - 23 February

  17 February - 23 February

  Lectures: Introduction to the course and mathematical modelling.

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  24 February - 2 March

  Lectures: Moore-Penrose pseudoinverse. Existence, proofs and examples.

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  3 March - 9 March

  Lectures: Moore-Penrose inverse, underdetermined systems with many and overdetermined systems with no solutions. 

  Introduction to vector functions. Tangent plane to a function of 2 variables.

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  Vector functions. Derivative/Jacobian matrix. Linear approximation. Tangent method. Newton method. 

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  17 March - 23 March

  Lectures: Gradient descent method. Curves and parametrisation of curves. Derivatives.

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  24 March - 30 March

  Lecture: Plotting plane curves, area bounded by the curve, arc length.

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  31 March - 6 April

  Lectures: Differential equations. Introduction and applications, separation of variables, first order linear ODE, variation of constants.

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  7 April - 13 April

  Lectures: Homogeneous DE. Exact DE. Systems of differential equations. Solving autonomous linear systems.

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  14 April - 20 April

  Lectures (Wednesday): Student's project presentation.

  Lectures (Thursday): Autonomous system of linear DE. Transforming an DE of higher order into a system of first order ODE.

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  21 April - 27 April

  Current week

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

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