Mathematical Physics 2
A.Y. 2021/2022
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
In case the emergency (pandemic) situation is still present when the course is give, teaching will adapt to the circumstances; if possible it will be in 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)
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
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)
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 preliminary test, and an oral exam.
- During the written test, 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. In special cases, the written test could be merged with the oral exam.
- 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.
- During the written test, 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. In special cases, the written test could be merged with the oral exam.
- 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
Lessons: 36 hours
Professors:
Boccato Chiara, Gaeta Giuseppe
Professor(s)