34831 - Physical-Mathematical Models for Industrial Engineering (2nd cycle)

Learning outcomes

The student must understand and apply some importantinstruments of advanced mathematics useful in engineering mechanical field.

Course contents

- Introduction on mathematical modeling                                                  - Review on ordinary differential equations
- Dynamical systems and applications
- The Fourier series
- The Fourier transform
- The Laplace transform
- Introduction to partial differential equations;
examples and applications of hyperbolic, elliptic and
parabolic-type equations
- Outlines on probability theory

Readings/Bibliography

1.T. Ruggeri, Introduzione alla Termomeccanica dei Continui, Monduzzi editore, 2007;

2.F. Bagarello, "Fisica Matematica", Zanichelli editore, Bologna, 2007;

3.S. Abenda, S. Matarasso, "Metodi Matematici", Societa' Editrice Esculapio, Bologna, 2003;

4.G. Borgioli, Modelli Matematici di Evoluzione ed Equazioni Differenziali, Celid editore, 1996;

5.S. Salsa, Equazioni a Derivate Parziali, Springer, 2004;

6.N. Tichonov, A. A. Samarskij, Equazioni della Fisica Matematica, edizioni Mir, 1981;

7.Sheldom M. Ross, Calcolo delle probabilità, Apogeo editore, 2004.

Teaching methods

Lessons with theory and exercises by means of blackboard and videoprojector.

Assessment methods

Due to national emergency situation for COVID19, there will be only an oral test, during about an hour (for the moment by online mode): in the first part, the student must show the ability of solving Fourier series, partial differential equations and probability problems, and then must have a discussion about some of the principal arguments of theory developed during the lessons, with particular attention to the methodological approach.

Teaching tools

Video projector.

Office hours

See the website of Leonardo Seccia