


Politecnico di Torino  
Academic Year 2007/08  
03AXQGI, 03AXQBN, 03AXQCJ, 03AXQCX Mathematical Physics 

Master of sciencelevel of the Bologna process in Physical Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Telecommunication Engineering  Torino 1st degree and Bachelorlevel of the Bologna process in Electronic Engineering  Torino Espandi... 





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: LoktaVolterra 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. 
