ANALYSIS FROM AN ADVANCED STANDPOINT
cod. 1007153

Academic year 2023/24
1° year of course - Second semester
Professor
- Marino BELLONI
Academic discipline
Analisi matematica (MAT/05)
Field
Formazione teorica avanzata
Type of training activity
Characterising
48 hours
of face-to-face activities
6 credits
hub:
course unit
in ITALIAN

Learning objectives

Deepen some selected topics in mathematical analysis.

Prerequisites

The analysis courses covered in the three-year degree.

Course unit content

The course aims to resume contents already covered by the student in the three-year degree, through different formulations and demonstrations that allow the grasp of aspects not previously explored in depth.

Full programme

Construction of real numbers. Equivalent formulations of the completeness axiom.
A generalization of trigonometric functions: the p-sine and p-cosine functions.
The Stone Weierstrass theorem.
Power series and Fourier series. Dirichlet and Fejer nuclei.
Riemann and Lebesgue integral. Integral by Daniell.

Bibliography

W. Rudin: Principles of Mathematical Analysis, McGraw-Hill

W. Rudin: Real and Complex Analysis, Boringhieri

H. Brezis: Analisi funzionale, Liguori

PDF notes from the lessons

Teaching methods

Frontal lessons.

Assessment methods and criteria

Written test with questions on the program covered in the course and a seminar on a topic agreed upon with the student.

Other information

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