Mathematics

General objectives: To acquire basic notions of harmonic analysis related to the continuous and discrete Fourier transform and Fourier series, and to know the main applications of these methods to both theoretical and practical problems. Specific objectives: Knowledge and understanding: by the end of the course the student will have acquired the main notions about continuous and discrete Fourier transform, Fourier series, wavelets, and their use in some theoretical and practical fields (differential equations, image processing, signal theory). Applying knowledge and understanding: at the end of the course the student will be able to solve basic level problems in harmonic analysis, will be familiar with Fourier transforms and Fourier series, and will be able to apply these techniques to the solution of various concrete problems. Critical and Judgmental Skills: the student will have the basis to understand when harmonic analysis techniques can be useful as tools for solving problems in various fields of analysis and its applications. Communication skills: ability to expose the contents in the oral part of the test and answer theoretical questions. Learning ability: the acquired knowledge will allow a study, individually or in a course, of more advanced aspects of harmonic analysis, and of more specific applicative topics.