Development of mathematical models for engineering and applied sciences with emphasis on real-world systems, deterministic, discrete, and stochastic models, introductory data-driven modeling approaches models formulation from physical principles, analysis of system behavior, models’ validation considering data, assumptions, uncertainty, and errors, dimensional analysis and scaling laws, dynamical systems, conservation laws, partial differential equations, and probabilistic modeling with basic reliability concepts, use of computational tools (MATLAB/Python) for simulation, visualization, and model evaluation.