## 20401813 - MATHEMATICAL METHODS FOR PHYISICS

Provide the student with some mathematical tools, especially with regard to the theory of complex variable functions and the Fourier analysis, which are
essential for the continuation of his training
teacher profile | teaching materials

Programme

Section I: Complex variable functions

- Complex numbers
- Analytic functions
- Integration of complex functions
- Power series
- Integration using the Residue theorem
- Asymptotic expansions
- Distributions

Section II: Vector spaces and eigenvalue problems

- Vector spaces
- Euclidean spaces
- Eigenvalue problems in N and infinite-dimensional vector spaces
- Function of a matrix
- Fourier transform

Section III: Integral and differential operators

- Integral operators and integral equations
- Sturm-Liouville operators
- First order partial differential equations

Core Documentation

C. Bernardini, O. Ragnisco and P.M. Santini
Metodi matematici della Fisica, NIS 1993

B. Chabat, M. Lavrentiev
Methodes de la Theorie des fonctions d'une variable complexe, MIR 1972

A. I. Markusevic
Elementi di teoria delle funzioni analitiche, Editori Riuniti 1988

F. Bagarello
Fisica Matematica, Zanichelli, 2007

P. A. Grassi
Esercizi di metodi matematici, Casa Editrice Ambrosiana, 2018

Type of delivery of the course

In order to achieve the expected goals, lessons will take place through taught classes on the board which will also provide a suitable number of exercises to allow the student to apply what they have learned to problems that can be easily found in physics. In the case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented. In particular, the lessons will be held remotely through the Microsoft Teams application, and any material related to the lectures uploaded on the Moodle platform.

Type of evaluation

teacher profile | teaching materials

Programme

Section I: Complex variable functions

- Complex numbers
- Analytic functions
- Integration of complex functions
- Power series
- Integration using the Residue theorem
- Asymptotic expansions
- Distributions

Section II: Vector spaces and eigenvalue problems

- Vector spaces
- Euclidean spaces
- Eigenvalue problems in N and infinite-dimensional vector spaces
- Function of a matrix
- Fourier transform

Section III: Integral and differential operators

- Integral operators and integral equations
- Sturm-Liouville operators
- First order partial differential equations

Core Documentation

C. Bernardini, O. Ragnisco and P.M. Santini
Metodi matematici della Fisica, NIS 1993

B. Chabat, M. Lavrentiev
Methodes de la Theorie des fonctions d'une variable complexe, MIR 1972

A. I. Markusevic
Elementi di teoria delle funzioni analitiche, Editori Riuniti 1988

F. Bagarello
Fisica Matematica, Zanichelli, 2007

P. A. Grassi
Esercizi di metodi matematici, Casa Editrice Ambrosiana, 2018

Type of delivery of the course

In order to achieve the expected goals, lessons will take place through taught classes on the board which will also provide a suitable number of exercises to allow the student to apply what they have learned to problems that can be easily found in physics. In the case of an extension of the health emergency from COVID-19, all the provisions that regulate the methods of carrying out the teaching activities and student assessment will be implemented.

Type of evaluation