Mathematical Physics 2
A.Y. 2023/2024
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 cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
1. First order PDEs and the method of characteristics
2. Wave equation. Solution by characteristics
3. Function spaces. Fourier series and Fourier transform.
4. Wave equation: solution by Fourier method
5. The heat equation by using Fourier analysis
6. Laplace equation or Schrödinger equation (depending on available time)
7. Introduction to fluid-dynamics (depending on available time)
2. Wave equation. Solution by characteristics
3. Function spaces. Fourier series and Fourier transform.
4. Wave equation: solution by Fourier method
5. The heat equation by using Fourier analysis
6. Laplace equation or Schrödinger equation (depending on available time)
7. Introduction to fluid-dynamics (depending on available time)
Prerequisites for admission
Fisica Matematica 1
Analisi Matematica 1,2,3
Geometria 1,2
Analisi Matematica 1,2,3
Geometria 1,2
Teaching methods
Lectures and exercise classes
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 and Oral exam
MAT/07 - MATHEMATICAL PHYSICS - University credits: 6
Practicals: 24 hours
Lessons: 36 hours
Lessons: 36 hours
Professors:
Boccato Chiara, Montalto Riccardo
Educational website(s)
Professor(s)
Reception:
Wednesday, 13.30-17.30
Room 1005, Department of Mathematics, Via Saldini 50, 20133, Milan