Modeling and Simulation

* Introduction and reminders: - the representation of reality: physical systems with mathematical models; - general concepts of systems analysis: characteristics, use and limitations of models; - Reminders of mathematics and linear algebra. * The descriptive models: - generalities and classification; - state, input and output, balance and stability, trajectory and motion. - linear systems: representation, study of equilibrium and stability. * Identification, simulation and prediction: - identification of a model: calibration and validation - simulation of a model and some examples of software; - methods of discretization of continuum models, basics of computing, dynamic error; - IN-OUT representation of linear systems, class ARMAX predictors. * Some special aspects: - cellular automa and neural networks; - analysis of data and signals: sampling and filtering. * The decision models: - generalities and classification; - linear programming: formulation and geometrical interpretation; - multi-objectives analysis: Pareto efficiency and methods of choice; - decisions in uncertain environment: selection criteria, Bayes theorem, decision tree. * Case planning and management: - discharge of pollutants; - agricultural plan of Sinai; - management of an environmental resource.