• Italiano
  • English

Department of Mathematics and Applications
"Renato Caccioppoli"


Real Analysis

Home > Exams > Real Analysis

Real Analysis

Credits

6

Prerequisites

None.

Scientific-disciplinary sector (SSD)

MAT/05 Mathematical Analysis.

Examination method

Oral exam.

Learning
objectives

The objectives of the course are: to deepen the concepts of integration and differentiation for non-smooth functions and to provide tools for the study of geometric properties of sets.

Syllabus

Functions of bounded variation and absolutely continuous functions (functions of one variable): properties. Functions of bounded variation (functions of several variables) and their properties. Hausdorff measure. Sets of finite perimeter and the isoperimetric inequality.

Expected learning
outcomes

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

  • know and understand the specific language of the discipline as well as the general issues relating to non-smooth functions;
  • are able to apply the knowledge acquired to the study and solution of concrete examples, making correct use of proof techniques;
  • 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 relating 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.