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

Learning verification occurs firstly by passing two written tests in November and January or, in the absence of a positive result for both proofs, by passing a written test. Both kinds of written exams last two hours and are organized in such a way for the student to solve three exercises chosen from a list of four. The written tests are aimed at verifying the level of effective understanding of the concepts and the students' ability to apply them in recurrent physics problems. All previous written examinations [from the 2017-2018 academic year] are available on the web-site of the course: http://dmf.matfis.uniroma3.it/fisica/triennale/scheda_corso.php?id=1179. The exam is approved if, in addition to the written assignments, the student will be able to pass an oral test based on questions extracted from the course program. 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: WRITTEN - PROOF The pre-selection written test will take place remotely through the use of the Microsoft Teams platform with the following methods: - the teacher will create a "meeting" on Teams and send the link to participate in the meeting ONLY TO THE OFFICIALLY REGISTERED STUDENTS IN GOMP; - once accepted the link, the student must identify himself by turning on the camera and microphone of his device; these will remain lit during the entire test; - the proof will be provided in the form of a pdf file provided at the established time (via the Teams platform); - the student must focus exclusively on the monitor, without distraction, avoiding move away from the webcam or other behavior that leads to believe the use of unauthorized media; - the teacher will ask the candidate to frame the table, on which there must be nothing outside the device used for the connection to Teams, white sheets for writing and pen, and the surrounding environment (the wall or the room depending how the desk is arranged) in order to verify that no other people are present; - the teacher will invite the candidate to position his video camera so that it is framed in "Half length portrait", including uncovered hands and ears in the frame, in order to verify that has no cell phone or notes, nor earphones with which to receive communications; - at the end of the two hours provided for the test, the test is declared closed and the student will have 10 minutes to send the exam to the teacher; she/he can scan the pages, all signed, or photograph the individual pages. The files thus obtained can be uploaded to Teams or, alternatively, sent by email to the teacher. In both cases, the official delivery time (shown in the Teams chat or in the email header) must not exceed two hours and ten minutes from the starting time. ORAL PROOF The oral exam will take place remotely through the use of the Microsoft Teams platform with the following methods: - the student is asked to have two devices equipped with a camera (for example PC and tablet); - the teacher will create a "meeting" on Teams and send the link to attend the meeting to the ONLY OFFICIALLY REGISTERED STUDENTS IN GOMP; given the request for two devices, each student will receive two invitations to two different email addresses, both previously uploaded to GOMP; - having accepted the link, the student must identify himself by turning on the camera and microphone of one of the available devices; these will remain lit during the entire test; - one of the two devices will be used to frame the student while the tablet can be used to write the answers to the questions in sharing mode on Teams (alternatively, in the absence of a tablet, this can be replaced by another tool equipped with camera that points on the sheet on which the student is writing); - the student will have to focus exclusively on the monitor, without distraction, avoiding to move away from the webcam or other behaviors that lead to believe the use of unauthorized supports; - the teacher will ask the candidate to frame the table, on which there must be nothing outside the devices used for the connection (or white sheets for writing and pen) and the surrounding environment (the wall or the room depending on how the desk is arranged) in order to verify that no other people are present; - the teacher will invite the candidate to position his video camera so that it is framed in "Half length portrait", including uncovered hands and ears in the frame, in order to verify that does not have additional cell phones / tablets or notes, nor earphones with which to receive communications. Please be advised that if the connection is lost during the oral exam, the interview will be recovered by formulating a new question. Please contact the teacher for any further clarifications.

Programme

see profile of the teacher holding the course

Core Documentation

see profile of the teacher holding the course

Type of delivery of the course

see profile of the teacher holding the course

Type of evaluation

see profile of the teacher holding the course