OVERVIEW

The course deals with basic topics of Numerical Analysis, with particular attention to the study of error, linear algebra and the solution of ordinary differential equations.

The theoretical topics are completed by laboratory experiences, using MatLab software. Using the "peer evaluation" technique (through workshops on Aulaweb) students evaluate some works produced during the laboratory experiences.

The lessons are held in Italian.

Language:  Italian.

AIMS AND CONTENT

LEARNING OUTCOMES

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 related to the treatment of data disturbed by error and to the analysis of methods for computing the solutions.

At the end of the course, the student should be able to deal with experimental data affected by error and  to interpret the elaborations of a computer starting from such data. Moreover the student should know the tools that allow to evaluate the efficiency and stability of the numerical methods for solving some mathematical problems, such as the solution of linear systems, the computation of the eigenvalues ​​of a matrix and the solutions of ordinary differential equations.

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 CFU (48 hours, II semester). In  presence in the classroom. However, should the health emergency continue, to safeguard everyone's health and safety, the theoretical lessons will be delivered online on the Teams platform. In this case, the lessons, delivered synchronously (live), are also recorded in such a way that each student can relate to the lessons, whenever he deems it appropriate. The slides used are published, at the end of each lesson, on Aulaweb.

In any case, innovative teaching methods are used such as:

    quiz on aulaweb
    glossary on aulaweb

which allow a better understanding of the course.

Laboratory exercises. 2 CFU (24 hours), the attendance of which is compulsory for 80% of the lessons (apart from exceptional cases of working students). In  presence in the PC laboratory. However, if the health emergency continues, to safeguard everyone's health and safety, the lessons will be delivered online on the Teams platform.
The exercices produced during these exercises will be subjected to "peer evaluation".

SYLLABUS/CONTENT

Error theory. Solution of linear systems: conditioning, Gauss' method and pivoting, matrix factorization: LU and Cholsky; applications. Eigenvalues: power method and extensions, similarity transformations, Householder transformation; QR factorization;  QR method. Approximation of functions: discrete least-squares: solution by means of normal equations. Singular Value Decomposition and application to the least-squaresproblem. Numerical solution of differential equations by means one step and multistep methods.

Laboratory: some exercises are proposed on topics addressed by the teacher in class to be carried out to groups of students, using the Matlab software. For each sheet, the writing of a report is required, corrected through the Peer review.

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

Exam Board

CLAUDIA FASSINO (President)

FABIO DI BENEDETTO

MICHELE PIANA (President Substitute)

LESSONS

LESSONS START

The class will start according to the academic calendar.

Class schedule

FOUNDATIONS OF NUMERICAL ANALYSIS

EXAMS

EXAM DESCRIPTION

Laboratory: The laboratory part is evaluated  on the basis of the "peer evaluation" of the works and of the final reports.

Quizzes: Solution of  quizzes on Aulaweb. This test provides the suitability to take the oral exam.

Oral exam: consisting in the discussion of the theoretical results presented in class.

The final grade consists in the grade of the oral exam plus a bonus due to the laboratory part.

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

ASSESSMENT METHODS

The discussion of the laboratory exercises  allows to evaluate the students' ability to work in groups, to implement the methods presented during the theoretical  lessons and  to interpret the results provided by the computer.

The oral exam will allow to verify the understanding of the theoretical concepts of applied mathematics, through questions aimed to analyze the ability to manage the various topics.

Exam schedule

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