B6359 - Mathematical Models for Industrial Engineering

Learning outcomes

The course focuses on the advanced mathematics areas which are most commonly used in mechanical and industrial engineering applications. At the end of the course the student is able to build, use and validate physical-mathematical models.

Course contents

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

Readings/Bibliography

Textbooks for further study:

1. K. F. Riley, M. P. Hobson, S. J. Bence, "Mathematical Methods for Physics and Engineering: A Comprehensive Guide", Cambridge University Press, 2006;
2. K. F. Riley, M. P. Hobson, “Student Solutions Manual for Mathematical Methods for Physics and Engineering”, Cambridge University Press, 2006;
3. T. Ruggeri, "Introduzione alla Termomeccanica dei Continui", Monduzzi editore, 2007;
4. F. Bagarello, "Fisica Matematica", Zanichelli editore, Bologna, 2007;
5. S. Abenda, S. Matarasso, "Metodi Matematici", Societa' Editrice Esculapio, Bologna, 2003;
6. G. Borgioli, "Modelli Matematici di Evoluzione ed Equazioni Differenziali", Celid editore, 1996;
7. S. Salsa, "Equazioni a Derivate Parziali", Springer, 2004;
8. N. Tichonov, A. A. Samarskij, "Equazioni della Fisica Matematica", edizioni Mir, 1981;
9. Sheldom M. Ross, "Calcolo delle probabilità", Apogeo editore, 2004.

Teaching methods

Lessons with theory and exercises by means of blackboard and videoprojector, stimulating students' interest through examples of engineering applications.

Assessment methods

The exam consists of an oral test, during about an hour: in the first part (about 1/2 hour), the student must show the ability of solving Fourier series, partial differential equations and probability problems, as showed during the lessons 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. During the exam the use of digital tools that exploit AI is in no way permitted. At the end of the exam a grade will be immediately assigned to the student. Students with temporary or permanent SLD or disabilities are invited to contact the responsible university office in advance (https://site.unibo.it/studenti-con-disabilita-e-dsa/it).

Teaching tools

Video projector and network connection.
Course notes for all the topics of the course in English and Italian.

Office hours

See the website of Leonardo Seccia