PRESENTAZIONE

The course deals with mathematical methods allowing to formalize and solve problems coming from the real world. For instance, the course will investigate how to model physical phenomena such as heat diffusion or wave propagation, as well as how to control in an optimal way a given process.

 

OBIETTIVI FORMATIVI

After the first part of the course the students will be able to use mathematical methods to describe real-world phenomena, such as heat diffusion and wave propagation. More specifically, they will be able to classify and manage the main analytical solution methods for linear partial differential equations, together with some techniques for their numerical solution. In the second part, the students will learn to manage multistage optimization problems by means of dynamic programming, which will be employed also to solve classical problems on graphs, such as the shortest path and shortest spanning tree, together with other algorithms.

OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO

After the first part of the course the students will be able to use mathematical methods to describe real-world phenomena, such as heat diffusion and wave propagation. More specifically, they will be able to classify and manage the main analytical solution methods for linear partial differential equations. In the second part, the students will learn to manage multistage optimal control problems by means of dynamic programming. Lastly, basic notions of nonlinear programming tools will be investigated to better understand their use in the first two parts of the course.
 

Modalità didattiche

Traditional lessons

 

PROGRAMMA/CONTENUTO

- Analytical solution of linear partial differential equations describing real-world phenomena.
- Dynamic programming for the solution of optimal control problems.
- Basic notions of nonlinear programming tools.

 

TESTI/BIBLIOGRAFIA

[1] D.P. Bertsekas, “Dynamic Programming and Optimal Control”, Athena Scientific, 2005.

[2] F.S. Hillier, G.J. Lieberman, “Introduction to Operations Research”, McGraw-Hill, 2001.

[3] R. Courant, D. Hilbert, “Methods of Mathematical Physics”, Interscience Publishers, 1973.

[4] R. Bracewell, “The Fourier Transform and its Applications”, McGraw Hill, 1999.

[5] P.V. O’Neil, “Advanced Engineering Mathematics”, Brooks Cole, 2003.

 

Commissione d'esame

MASSIMO PAOLUCCI (Presidente)

MAURO GAGGERO (Presidente)

Modalità didattiche

Traditional lessons

 

INIZIO LEZIONI

Come da Calendario didattico

Modalità d'esame

The examination mode consists of an oral test to ensure learning of the course content.

Modalità di accertamento

The oral exam focuses on the learning of one or two subjects from those discussed in class.