Mathematical Physics 2

A.Y. 2025/2026
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.
Single course

This course can be attended as a single course.

Course syllabus and organization

Single session

Responsible
Lesson period
First semester
Course syllabus
1. First order partial differential equations and characteristic method
2. Wave equation on the real line
3.Hilbert spaces, Fourier series and Fourier transform.
4.Wave equations on intervals. Fourier methods
5. Heat equations on intervals and on the real line. Fourier methods
Prerequisites for admission
MATHEMATICAL ANALYSIS 1,2,3,4

MATHEMATICAL PHYSICS 1
Teaching methods
LECTURES
Teaching Resources
1) Walter Strauss. Partial Differential Equations, an introduction.

2) Elias Stein, Rami Shakarchi. Fourier Analysis. An introduction. PRINCETON LECTURES IN ANALYSIS

3) Walter Craig. A course on Partial Differential Equations. Graduate studies in mathematics 197. American Mathematical Society.

4) Sandro Salsa. Equazioni a derivate parziali. Metodi, Modelli e Applicazioni. Springer Verlag Italia, 2010
Assessment methods and Criteria
WRITTEN EXAM (3-4 EXERCISES)

ORAL EXAM
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Practicals: 24 hours
Lessons: 36 hours
Professor(s)
Reception:
Wednesday, 13.30-17.30
Room 1005, Department of Mathematics, Via Saldini 50, 20133, Milan