• Italiano
  • English

Department of Mathematics and Applications
"Renato Caccioppoli"


Mathematical Analysis 3

Home > Exams > Mathematical Analysis 3

Mathematical Analysis 3

Credits

6

Prerequisites

Mathematical Analysis 2.

Scientific-disciplinary sector (SSD)

MAT/05 Mathematical Analysis.

Examination method

Written exam (exercises and numerical problems, possibly multiple-choice) and oral exam.

Learning
objectives

Introduction to Fourier series, Fourier transforms, functional analysis and Lebesgue measure.

Syllabus

Fourier series expansions: pointwise and uniform convergence. Lebesgue measure. Lp spaces. Hilbert spaces. Fourier transform in R. Introduction to functional analysis.

Expected learning
outcomes

At the end of the course, students must demonstrate that they

  • know and understand the main results of functional analysis and Lebesgue measure;
  • are able to apply the knowledge acquired to solving ordinary differential equations, with particular regard to evolution phenomena;
  • are able to communicate ideas and solutions clearly, rigorously and effectively to both specialist and non-specialist audiences;
  • are able to identify the most appropriate methods to analyse and solve a problem related to the course topics and to interpret the results correctly.

Learning outcomes
to be assessed

Command of the knowledge acquired, clarity of presentation, rigour in the use of language, confidence in using the notions acquired.