AIMS AND CONTENT

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 or remote (through Teams) lectures (50 hours), including some MATLAB demonstrations.

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).
Optimization algorithms (gradient descent).
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

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

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 divided in two parts; each of them is referred to a half of the program. Each part consists in the explanation of one topic chosen by the student and one topic chosen by the teacher. The total score is 30.

ASSESSMENT METHODS

The exam aims at verifying that the student:

•    can communicate his/her thoughts properly, synthetically and with an adequate technical terminology;
•    demonstrates his/her knowledge and comprehension of the subject topics.

Exam schedule