The course covers basic topics of Numerical Analysis, with particular attention to the study of error, linear algebra and the solution of ordinary differential equations. The arguments developed in theory are complemented by experiences in the laboratory, using the MatLab software.
Language: Italian.
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.
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.
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
Traditional: The course consists of 8 CFU, divided as follows (in the same semester):
6 CFU of theory in the classroom (48 hours) whose frequency is recommended but not mandatory;
2 CFU of laboratory lessons (24 hours) whose attendance is compulsory for 80% of the lessons (apart from the exceptional cases of working students).
The course is supported by the use of AulaWeb
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: 5 exercises about topics addressed during the semester (the use of Matlab is required)
Lecture notes, written by Fassino and Piana, available on AulaWeb.
Book: Bini, Capovani, Menchi: “Metodi Numerici per l’Algebra Lineare". Ed. Zanichelli
Ricevimento: By appointment by sending an email to fassino at dima.unige.it
Ricevimento: Office hours by appointment via email
CLAUDIA FASSINO (President)
MICHELE PIANA (President)
FABIO DI BENEDETTO
The class will start according to the academic calendar.
FOUNDATIONS OF NUMERIC ANALYSIS
Laboratory tests: discussion of two of the exercises done during the course, one preassigned before the discussion and one chosen by the teacher during the discussion; the presence of all the members of the group is required. The test must be carried out before the oral exam and in any case before the end of June. Individual assessment, if positive, will be: S (18-21 / 30th) D (22-24) B (25-27) O (28-30) O + (30L)
Written exam: solution of an exercise. Passing this test is necessary to access the oral exam.
Oral exam: the exposition of the theoretical notions..
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.
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
