CODE 66454 ACADEMIC YEAR 2024/2025 CREDITS 8 cfu anno 2 MATEMATICA 8760 (L-35) - GENOVA SCIENTIFIC DISCIPLINARY SECTOR MAT/08 LANGUAGE Italian TEACHING LOCATION GENOVA SEMESTER 2° Semester TEACHING MATERIALS AULAWEB OVERVIEW 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. Language: Italian. AIMS AND CONTENT LEARNING OUTCOMES The teaching aims to offer the mathematical and methodological concepts underlying the techniques of scientific computation. An integral part of the course should be considered laboratory exercises where the student experiments and verifies the theory done in class. 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. In the laboratory, using the MatLab software, the student will acquire the ability to implement the algorithms illustrated during the theoretical lessons and the ability to evaluate the results obtained, identifying the sources of error due to inherent and algorithmic errors. Furthermore, thanks to the experience of peer evaluation, the student will have refined functional literacy competence, personal competence, social competence and the ability to learn to learn. PREREQUISITES 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 TEACHING METHODS 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". The final grade is given by a weighted average between the oral grade (preponderant) and the peer evaluation grade. SYLLABUS/CONTENT Frontal lessons. 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. RECOMMENDED READING/BIBLIOGRAPHY 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 Ricevimento: By appointment by sending an email to fassino at dima.unige.it FEDERICO BENVENUTO Exam Board CLAUDIA FASSINO (President) MICHELE PIANA FEDERICO BENVENUTO (President Substitute) FABIO DI BENEDETTO (Substitute) PAOLA FERRARI (Substitute) LESSONS LESSONS START The class will start according to the academic calendar. Class schedule The timetable for this course is available here: Portale EasyAcademy EXAMS EXAM DESCRIPTION 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. There will be 2 exam sessions available for the winter session (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. 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. Students with disabilities or specific learning disorders (DSA) are reminded that in order to request adaptations during the exam, they must follow the instructions described in detail on Aulaweb https://2023.aulaweb.unige.it/ course/view.php?id=12490#section-3. In particular, concessions must be requested significantly in advance (at least 10 days) of the exam date by writing to the teacher with a copy of the School Contact teacher and the competent office (see instructions). ASSESSMENT METHODS 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) . Exam schedule Data appello Orario Luogo Degree type Note 23/01/2025 09:00 GENOVA Orale 11/02/2025 09:00 GENOVA Orale 09/06/2025 09:00 GENOVA Orale 14/07/2025 09:00 GENOVA Orale 17/09/2025 09:00 GENOVA Orale FURTHER INFORMATION 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 Agenda 2030 - Sustainable Development Goals Quality education Gender equality Decent work and economic growth