ISTITUZIONI DI FISICA MATEMATICAModule MODULO I
Academic Year 2024/2025 - Teacher: Orazio MUSCATOExpected 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
The BGK model
Textbook Information
[1] V.I. SMIRNOV, Corso di matematica superiore II, Editori Riuniti.
[2] S. Salsa, Equazioni a derivate parziali, Springer
[3] C. Cercignani, The Boltzmann equation and its applications, Springer-Verlag
[4] appunti del docente
Course Planning
| Subjects | Text References | |
|---|---|---|
| 1 | Vibrating string equation and physical interpretation of the results | 1,2,4 |
| 2 | Heat equation | 1,2,4 |
| 3 | Laplace equation | 1,2,4 |
| 4 | Poisson equation | 1,2,4 |
| 5 | Boltzmann equation | 3 |
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.