# ISTITUZIONI DI FISICA MATEMATICAModule MODULO I

**Academic Year 2023/2024**- Teacher:

**Orazio MUSCATO**

## Expected Learning Outcomes

1. Give the basic elements of the partial differential equations of mathematical physics.

2. Understanding of physical phenomena governed by partial differential equations; Construction of mathematical models: equations of the waves, heat, Laplace and Boltzmann equation.

3. Understanding of the different solution methods: why it has been proposed a solution method? What are some other alternative methods? Understanding how the analytical solutions obtained are interpreting the physical real situations (wellposedness of the models or paradoxes).

4. It will be privileged the undertsnding the physical part, the models and their analytical solution.

## Course Structure

Equazioni differenziali della Fisica Matematica - 6 CFU - 47 hours

Lectures and exercises done by students at home and in class.

Should teaching be carried out in mixed mode or remotely, it may be necessary to introduce changes with respect to previous statements, inline with the programme planned and outlined in the syllabus.

## Required Prerequisites

## Detailed Course Content

Partial differential equations

Scalar conservation laws and first order partial differential equations

Second order semilinear equations in two variables

Heat equation

Diffusion and probability

Vibrating string equation

Laplace and Poisson equations

An introduction to the kinetic theory of gases

Boltzmann equation

Reversibility paradox

Method of moments

## Textbook Information

[1] M.M. SMIRNOV, Second-Order partial differential equations, ed. Noordhoff.

[2] F.JOHN, Partial differential equations, Springer-Verlag.

[3] V.I. SMIRNOV, Corso di matematica superiore II, Editori Riuniti.

[4] N.S.KOSHLYAKOV, M.M.SMIRNOV, E.B.GLINER, Differential equations of mathematical physics, ed. North-Holland.

## Course Planning

Subjects | Text References | |
---|---|---|

1 | Vibrating string equation and physical interpretation of the results | 1,2 |

2 | Heat equation | 1,2 |

3 | Laplace equation | 1,2 |

4 | Poisson equation | 1,2,3 |

5 | Boltzmann equation | 4 |

## Learning Assessment

### Learning Assessment Procedures

The final exam consists of an oral test during which the candidate demonstrates that he has assimilated the topics covered in the course (understanding, reasoning and the ability to build examples will be privileged).

Verification of learning can also be carried out electronically, should the conditions require it.