Mathematical Physics 2
A.Y. 2025/2026
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.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
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
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
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
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
ORAL EXAM
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Practicals: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professors:
Giacomelli Emanuela Laura, Montalto Riccardo
Professor(s)
Reception:
Wednesday, 13.30-17.30
Room 1005, Department of Mathematics, Via Saldini 50, 20133, Milan