Mathematical Physics 2

A.Y. 2020/2021
6
Max ECTS
60
Overall hours
SSD
MAT/07
Language
Italian
Learning objectives
Master methods of solution for linear constant coefficients PDE of first and second order, in particular those relevant in Mathematical Physics (e.g. waves and heat): Fourier analysis and Green function.
Expected learning outcomes
The student will learn the method of characteristics, the basic aspects of Fourier analysis and the method of Green function (propagator). This tools, or paramount relevance for the continuation of his/her studies, will be here applied to the solution of some fundamental equations for the Mathematical Physics of continuous media.
Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Lectures and exercise classes will mostly be given in synchro mode, unless tecxhnical problems prevents this; it is however possible that some lectures and exercises classes will be given in a-synchro mode.
Course syllabus
1. Quasi-linear PDEs and the method of characteristics
2. Wave equation. Solution by characteristics
3. Function spaces. Fourier series and transform.
4. Wave equation: solution by Fourier method
5. The heat or diffusion equation. Propagator
6. Laplace equation (depending on available time)
7. Some non-linear equations of Mathematical Physics (depending on available time)
Prerequisites for admission
Fisica Matematica 1
Analisi Matematica 1,2,3
Geometria 1,2
Teaching methods
Lectures and exercise classes
Teaching Resources
V.I. Smirnov, Corso di Matematica Superiore vol. 2 (Editori Riuniti)
G. Cicogna, Metodi Matematici della Fisica (Springer Italia)
Byron & Fuller, Mathematical Methods of Physics (Dover)
Lecture Notes (in Italian)
Assessment methods and Criteria
The final examination consists of two parts: a written exam, and an oral exam.

- During the written exam, the student must solve some exercises in the format of open-ended and/or short answer questions, with the aim of assessing the student's ability to solve problems. The duration of the written exam will be proportional to the number of exercises assigned, also taking into account the nature and complexity of the exercises themselves (however, the duration will not exceed three hours). The outcomes of these tests will be available in the SIFA service through the UNIMIA portal.
- The oral exam can be taken only if the written component has been successfully passed. In the oral exam, the student will be required to illustrate results presented during the course and will be required to solve problems in order to evaluate her/his knowledge and comprehension of the arguments covered as well as the capacity to apply them.


The complete final examination is passed if the two parts (written, oral) are successfully passed. Final marks are given using the numerical range 0-30, and will be communicated immediately after the oral examination.
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Practicals: 24 hours
Lessons: 36 hours
Educational website(s)
Professor(s)
Reception:
on (e-mail) appointment
office in Dept. of Mathematics
Reception:
Wednesday, 13.30-17.30
Room 1005, Department of Mathematics, Via Saldini 50, 20133, Milan