Politecnico di Torino
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Politecnico di Torino
Academic Year 2007/08
03AXQGI, 03AXQBN, 03AXQCJ, 03AXQCX
Mathematical Physics
Master of science-level of the Bologna process in Physical Engineering - Torino
1st degree and Bachelor-level of the Bologna process in Telecommunication Engineering - Torino
1st degree and Bachelor-level of the Bologna process in Electronic Engineering - Torino
Espandi...
Teacher Status SSD Les Ex Lab Tut Years teaching
Bellomo Nicola ORARIO RICEVIMENTO     3 1 0 0 8
SSD CFU Activities Area context
MAT/07 4 D - A scelta dello studente A scelta dello studente
Objectives of the course
The course aims to provide the basic knowledge on modelling and to mathematical methods related to the analysis of models, with special attention to models in physics and technology. Special attention is given to the analysis of complex systems.
Prerequisites
Differential calculus and foundations of probability theory
Syllabus
The program is organized through four parts:

1: Scaling and modelling methods ' Classification of models and equations of mathematical physics ' Simple examples of models at the microscopic and macroscopic scale.

2: Modelling at the microscopic scale ' Examples: Lokta-Volterra systems; dynamical systems in mechanics ' Mathematical problems for models described by ordinary differential equations. Scientific softwares to solve the initial value problem for o.d.e.

3: Modelling at the macroscopic scale ' Examples: hydrodynamical models, diffusion models, wav e propagation - Classification of partial differential equations and mathematical problems for models described by p.d. equations. Scientific softwares to solve initial and boundary value problems for p.d. equations.

4: Complex systems in applied sciences ' Examples: social dynamics; multiparticle systems; semiconductor modelling - The master equation approach to modelling collective behaviours from microscopic interactions. Introduction to models of the kinetic theory.
Laboratories and/or exercises
Problem solving with reference to the application of models to the analysis of systems of real world.
Bibliography
N. Bellomo e L. Preziosi, Modelling, Mathematical Methods and Scientific Computation, CRC Press, Boca Raton, (1995).
N. Bellomo, E. De Angelis, M. Delitala, Equations of Mathematical Physics and Applied Sciences, (2005) - Electronic book to be downloaded.

Programma definitivo per l'A.A.2006/07
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