Note del corso opzionale 66698 - COMPLEMENTI DI ANALISI MATEMATICA (laurea triennale).
The notes might be loosely related to the course 28393 - ANALISI FUNZIONALE 1 (2023) for the Bachelor in Mathematics, and they have also been used in courses at the Curtin University (Western Australia). In fact, they are a comprehensive introduction to Real Analysis. The book chapters are (1) Normed spaces, (2) Banach and Hilbert spaces, (3) Measure thery and Lebesgue integral, (4) L^p spaces, (5) distributions, (6) Fourier transform, (7) linear partial differential equations, (8) Laplace transform, (9) Fourier series.
Le note coprono i corsi 10832 - PROBABILITÀ E STATISTICA MATEMATICA (laurea triennale) e 17266 - PROCESSI STOCASTICI (laurea magistrale, curriculum generale).
Note per il corso 46146 - ANALISI NON LINEARE, Laurea Magistrale, indirizzo generale
Notes for the course 96756 - ADVANCED MATHEMATICAL ANALYSIS (Master in Mathematics for Applications). The main focus of the course is on measure theory, and it includes foundational results on Radon measures. The basics of functional analysis, Fourier theory, and tempered distributions, are also covered.
Note per il corso opzionale B0323 - ANALISI FUNZIONALE E TEORIA DEGLI OPERATORI, laurea magistrale, curriculum generale. The notes cover the basics of functional analysis, compact operators, Gelfand theory, and the spectral theorem for (not necessarily bounded) self-adjoint operators.
Here you find the lecture notes for the 1st module of the course B9075 - TOPICS IN HOLOMORPHIC FUNCTION THEORY.
The notes are work in progress. If you find gaps or mistakes, please let me know.
Here you find Cauchy's 1825 Mémoire, and the slides of a seminar by Nikolaos Chalmoukis on Cauchy's contributions to holomorphic function theory.