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

The course focuses on three different topics: dynamic optimization, nonlinear programming, and partial differential equations.

In more detail, students will learn how to formalize and solve dynamic optimization problem via dynamic programming. Then, they will analyze the formalization and solution of static decision problem using nonlinear programming. Lastly, they will investigate the use of mathematical methods to describe real-world phenomena, such as heat diffusion and wave propagation, and the main analytical solution methods.

For all arguments, the focus will be on both methodological concepts and application examples. The various concepts are explained via traditional lessons.

Modalità didattiche

Traditional lessons.

PROGRAMMA/CONTENUTO

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

TESTI/BIBLIOGRAFIA

Handouts in electronic format provided by the lecturer.

Books for additional details:

[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

MAURO GAGGERO (Presidente)

MASSIMO PAOLUCCI (Presidente)

MARCELLO SANGUINETI

Modalità didattiche

Traditional lessons.

INIZIO LEZIONI

As reported in the official calendar.

Modalità d'esame

The exam consists of an oral interview to ensure learning of the course content.

Modalità di accertamento

Learning will be assessed by a number of oral questions regarding the various topics addressed in the course.

Calendario appelli