MATHEMATICAL METHODS APPLIED TO THE ENVIRONMENT

Knowing how to construct and understand mathematical models that describe qualitatively and quantitatively some phenomena related to the environment. Knowing how to use mathematical tools, such as combinatorics, discrete probability, differential equations and some optimization methods in order to realize some mathematical related to Biology and Environmental Sciences.

General information on mathematical models.

PART A - Discrete models. Notions of combinatorics and discrete probability. Fibonacci model. Cell duplication. A model for dynamics diseases. Models in Genetics: examples, inbreeding, natural selection, genetics of bacteria: plasmids. Latin squares and their applications. Outlines of discrete dynamical systems.

PART B - Continuous models. Elements of differential calculus and some complements. Elements of constrained optimization. Differential equations of the first and second order. Partial Differential Equations (essential nomenclature). Models in Ecology. Models for air pollution propagation. Models of water pollution propagation. Models of non-renewable resources. Models of environmental protection. Models for the Global Dynamics. Models used in hydraulics. Models of landscape evolution. Models of glaciers and shallow ice approximation.

1. V. Comincioli – Modelli matematici. Elementi introduttivi – Università degli studi di Pavia
2. N. Hritonenko, Y. Yatsenko - Mathematical Modeling in Economics, Ecology and the Environment. Second edition – Springer (2013)
3. A. Fowler – Mathematical Geoscience – Springer (2011)
4. Dispense distribuite dal Docente