CdSMATEMATICA

Codice062AA

CFU6

PeriodoSecondo semestre

LinguaItaliano

Advanced use of languages like Matlab and Octave. Ability to use these languages to solve mathematical models. Familiarity with the process of creating a mathematical model from problems of the real world.

Designing optimized functions in Matlab/Octave and solving different mathematical models and problems with the help of Matlab / Octave

At the end of the course students will be able to analyze mathematical problems with graphical tools, solving ordinary differential equations modeling problems in applied sciences, facing problems related to the Web and to image restoration.

Designing optimized functions in Matlab/Octave and completing projects from the level of the modelization of a problem to the design of a solution algorithm and its implementation.

Familiarity with mathematical modeling, with computational aspects, with efficient implementation of the software

Solving different exercises by analyzing models and designing software

Basic notions in Linear Algebra, Analysis, Numerical Analysis, basic knowledge of Matlab / Octave

The Page Rank problem and the Page Rank algorithm: the power method. Recommendation systems. The Singular Values Decomposition: application to image compression, application to image recognition. Graphical analysis of Prime numbers: the Ulam spiral and other constructions. Graphical representation of functions of complex variable. Fixed point iterations: creating basins of attraction and fractals, Julia sets. The Arnold cat: a way for image criptography. The Fast Fourier Transform and its application to signal and image filtering. A model for image restoration: point-spread functions and solving large structured systems, the problem of regularization. Numerical solution of ordinary differential equations by means of Matlab, applications to different models from the Real World.

Lecture notes from the lecturers.

Students who cannot attend the lectures are requested to solve all the exercises proposed in the class, downloadable from the web page of the course, and an additional project which will be proposed directly by the lecturers.

Assessment is performed through the correctness of the exercises proposed in the class during the lectures, and through the individual work performed at home.