AIMS AND CONTENT

LEARNING OUTCOMES

The main objective of the course is to present the theoretical background to formulate models starting from experimental data. Basic notions are introduced about mathematical models, numerical calculus, regularization, and numerical simulation of dynamical systems. Moreover, the course presents the fundamental notions about data classification and variational calculus.

AIMS AND LEARNING OUTCOMES

At the end of the course, the student will know the numerical methods for approximation, differentiation, and integration of functions, the solution of ordinary differential equations systems, the singular values decomposition of matrices, the optimization. He/she will also know the variational methods and their application to modeling.

TEACHING METHODS

Classroom lectures (50 hours), including some MATLAB demonstrations to facilitate the reaching of the expected learning outcomes.

SYLLABUS/CONTENT

Normed spaces, orthonormal spaces, operators.
Function approximation on a normed space, best approximation.
Numerical differentiation.
Numerical integration.
Methods for the numerical solution of ordinary differential equations (ODE).
Compatible and non compatible linear systems.
Least squares method.
Singular value decomposition (SVD) with applications.
Condition of a linear system.
Linear and nonlinear classification techniques.
Functionals.
Variational calculus: differential of a functional, Euler-Lagrange equations.
Applications of the variational calculus for modelling.

RECOMMENDED READING/BIBLIOGRAPHY

Notes by the teacher, available also for non-attending students.

Mauro Parodi: “Metodi matematici per l’ingegneria” Levrotto&Bella ed., Torino, 2013.

Students with disabilities or learning diseases may contact the teacher if they need specific books or notes.

TEACHERS AND EXAM BOARD

Exam Board

ALBERTO OLIVERI (President)

RICCARDO BERTA (President Substitute)

EDOARDO RAGUSA (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/8732/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

The exam is oral and divided in two parts; each of them is referred to a half of the program. Each part assigns a maximum score of 15. The final score is the sum of the two partial scores.

ASSESSMENT METHODS

The oral exam will verify the comprehension of the topics explained during the lectures, the ability to synthesize concepts, and the use of a proper technical language.

Exam schedule

FURTHER INFORMATION

Students with disabilities or learning disorders (e.g., DSA) can request special exam modalities, which will be defined individually with the "Referente per Ingegneria del Comitato di Ateneo per il supporto agli studenti disabili e con DSA". The interested students are invited to contact the teacher and the "Referente per Ingegneria" (https://unige.it/commissioni/comitatoperlinclusionedeglistudenticondisabilita.html), without sending documents about their disability.