|SCIENTIFIC DISCIPLINARY SECTOR
The course deals with basic topics of Numerical Analysis, with particular attention to the study of error, numerical linear algebra and the solution of ordinary differential equations.
The topics carried out in theory are complemented by laboratory experiences, using the MatLab software. Using the "peer evaluation" technique, the students evaluate some works produced during the laboratory experiences.
AIMS AND CONTENT
The course aims to offer the mathematical and methodological notions that are the basis of the techniques of scientific calculus. An integral part of the course is to consider the laboratory exercises where the student experiences and verifies the theory presented in the theoretical part.
AIMS AND LEARNING OUTCOMES
The learning outcomes consist in creating a more applicative mathematical point of view, aimed at solving problems deriving from the observation of the real world, with particular attention to the problems relating to the treatment of data disturbed by errors and to the analysis of methods of approximation of the solutions. At the end of the course, the student will be able to deal with experimental data affected by errors, to interpret the processing of a computer starting from such data and to know the tools that allow to evaluate the efficiency and stability of methods for approximation of the solution of some mathematical problems, such as the solution of linear systems, the calculation of the eigenvalues of a matrix and the solution of ordinary differential equations. Furthermore, thanks to the experience of peer evaluation, the student will refine functional literacy competence, personal competence, social competence and the ability to learn to learn.
Knowledge of basic concepts of analysis, such as continuity and derivability of the functions, Taylor development, ordinary differential equations, and linear algebra, such as matrices, vectors, linear systems.
Furthermore, knowledge of the MatLab software is required
Theoretical lessons: 6 credits (48 hours in the second semester). In presence in the classroom. In his/her personal work the student will acquire the basic knowledge and concepts of Numerical Analysis and he/she will be able to solve exercises. A set of quizzes on Aulaweb allows for better use of the course and the possibility of self-assessing one's preparation.
Laboratory part. 2 credits (24 hours), related to the topics covered in class, whose attendance is compulsory for 80% of the lessons (apart from the exceptional cases of working students). The laboratory provides for the development, in groups, of 4 sheets of exercises using the computer and the MatLab language. Furthermore, each group will write a report on an exercise sheet assigned by the teacher. The reports will be subjected to the innovative teaching technique of "peer evaluation".
Upon passing the exam, students will receive an Open Badge to certify their participation in the "peer evaluation".
- Error theory: conditioning and stability.
- Solution of linear systems: conditioning, Gauss method with pivoting strategy, matrix factorizations: LU and Cholesky and applications.
- Eigenvalues: power method and its variants, transformations by similarity and Householder transformations: QR factorization, outline of the QR method.
- Approximation of functions: discrete least squares: resolution using normal equations.
- Singular value decomposition and applications to the problem of discrete least squares.
- Numerical solution of differential equations using one-step and multistep methods.
Laboratory. Some exercise sheets on topics covered in class are proposed, to be carried out in groups in the computer room with the aid of the Matlab software. Furthermore, each group is required to draft a report relating to a specific exercise sheet, corrected through Peer Evaluation.
Lecture notes, written by Fassino and Piana, available on AulaWeb.
Book: Bini, Capovani, Menchi: “Metodi Numerici per l’Algebra Lineare". Ed. Zanichelli
TEACHERS AND EXAM BOARD
CLAUDIA FASSINO (President)
FABIO DI BENEDETTO
MICHELE PIANA (President Substitute)
PAOLA FERRARI (Substitute)
The class will start according to the academic calendar.
L'orario di tutti gli insegnamenti è consultabile all'indirizzo EasyAcademy.
The exam consists of a single oral part, consisting of the presentation of some of the theoretical results developed in class. To access the oral exam, the student must have obtained a pass in all the quizzes on Aulaweb. This eligibility does not expire.
The laboratory part is evaluated on the basis of the "peer evaluation" of the reports and on the basis of the final version of the reports.
The final grade is evaluated as follows: 0.3 laboratory grade + 0.8 oral grade.
Students with DSA, disability or other special educational needs certification are advised to contact the teacher at the beginning of the course to agree on teaching and exam methods which, in compliance with the teaching objectives, take into account the learning methods individuals and provide suitable compensatory instruments.
There will be 2 exam sessions available for the winter session (mid-January-February) and 3 exam sessions for the summer session (June, July and September). Extraordinary exam sessions will not be granted outside the periods indicated in the study course regulations, with the exception of non-course students.
Details on how to prepare for the exam and on the degree of detail of each topic will be given during the lessons. The oral exam will mainly focus on the topics covered during the lectures and will aim to evaluate not only if the student has reached an adequate level of knowledge, but if he/she has acquired the ability to explain mathematical concepts (definitions, theorems and proofs) in clearly and in correct terminology. The laboratory part will have the aim of evaluating the students' ability to work in a group, to implement the methods seen in class, to present them in a report and to evaluate the work of others (and consequently their own) .
|riservata agli studenti iscritti a.a.2022/23 e aa.aa. precedenti
|riservata agli studenti iscritti a.a.2022/23 e aa.aa. precedenti
Prerequisites: Notions of Analysis (functions, derivatives and hints on differential equations) and of Linear Algebra (matrices, vectors, linear systems).
The use of the MatLab software.
Lesson attendance: recommended for the theoretical lessons in the classroom and mandatory for laboratory lessons (unless documentation proving the impossibility to attend)
Registration for the exams: online