This repository contains MATLAB solutions for laboratory assignments and major projects completed as part of the Modelowanie Matematyczne (Mathematical Modelling) course (2024Z / Winter Semester 2024) at the Faculty of Mathematics and Information Science (MiNI), Warsaw University of Technology (Politechnika Warszawska).
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lab03–lab09: Laboratory exercises covering foundational mathematical modelling techniques in MATLAB, including numerical integration, solving differential equations, phase space analysis, and dynamic systems. -
projekt1: Analytical and Numerical Solutions of ODE Systems- Symbolic solution using MATLAB's
dsolve. - Implementation of a custom 3-stage implicit Runge-Kutta numerical solver based on the Butcher tableau.
- Convergence rate and error analysis across varying integration step sizes (
$h$ ).
- Symbolic solution using MATLAB's
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projekt2: Three-Body Problem: Parameter Optimization and Trajectory Simulation- Physical modeling of 3-body gravitational interaction dynamics.
- Parameter estimation (unknown body mass and initial velocities/positions) minimizing Mean Squared Error (MSE) via gradient calculations and MATLAB's
fminsearch. - High-precision trajectory prediction using
ode45.
- Language / Environment: MATLAB (R2024a or compatible)
- Toolboxes Used:
- Symbolic Math Toolbox
- Optimization Toolbox