Mathematical Modelling
섹션 개요
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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:
- Linearni modeli: sistemi linearnih enačb, posplošeni inverzi matrik
- Nelinearni modeli: vektorske funkcije vektorske spremenljivke, sistemi nelienarnih enačb, krivulje in ploskve
- Krivulje in ploskve
- 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:
- Linear models: systems of linear equations, generalized inverses of matrices
- Nonlinear models: vector functions of a vector variable, nonlinear systems, curves and surfaces
- Curves and surfaces
- Dynamic models: differential equations and dynamical systems
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Lectures: Introduction to the course and mathematical modelling.
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Lectures: Moore-Penrose pseudoinverse. Existence, proofs and examples.
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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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Lectures: Gradient descent method. Curves and parametrisation of curves. Derivatives.
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Lecture: Plotting plane curves, area bounded by the curve, arc length.
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Lectures: Differential equations. Introduction and applications, separation of variables, first order linear ODE, variation of constants.
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Lectures: Homogeneous DE. Exact DE. Systems of differential equations. Solving autonomous linear systems.
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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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Lectures: Differential equations - Applications, separation of variables, first order linear ODE, variation of constants,
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Jupyter Notebook, to be opened locally.
2025/04/21 22:07 업로드됨 -
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Lab sessions: Backward Euler method, example derivation of a Runge-Kutta method. More DEs.
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Lab sessions: Solving systems of nonlinear equations, part 2. Automatic differentiation.
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Jupyter Notebook, to be opened locally.
2025/05/13 06:04 업로드됨 -
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Alternative approaches to solving F(X) = 0 (without automatic differentiation).
2025/05/20 19:13 업로드됨
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Lab sessions: First order linear systems. Homogeneous systems with constant coefficients. Approximation of autonomous systems (Lotka-Volterra example).
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Jupyter Notebook, to be opened locally.
2025/05/19 18:22 업로드됨 -
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Lab sessions: The Lorenz system and deterministic chaotic behavior. Determination of periodic orbits.
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Jupyter Notebook, to be opened locally.
2025/05/26 21:07 업로드됨 -
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