- Docente: Nicola Arcozzi
- Credits: 6
- SSD: MAT/05
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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from Sep 21, 2023 to Dec 22, 2023
Learning outcomes
At the end of the course, students will possess the knowledge of the main instruments of advance mathematical analysis: Sobolev spaces, spaces of generalized functions, Fourier transform. These tools will be the main instruments necessary to the quantitative and qualitative study of properties of the solutions to PDEs.
Course contents
Metric spaces (with emphasis on completess)
Measure theory
Hilbert space/Fourier series
Basic Functional Analysis
Readings/Bibliography
Lecture notes on Virtuale
Suggested reading:
Richard F. Bass, Real Analysis for Graduate Students Version 4.3, 2022 https://bass.math.uconn.edu/real.html
Gerald B. Folland, Real Analysis: Modern Techniques and Their Applications 2nd Edition, Wiley 1999
Michael Reed, Barry Simon, Functional Analysis, 1981
Walter Rudin, Real and Complex Analysis, McGraw-Hill 1986
Terence Tao, An Introduction to Measure Theory, AMS 2011 https://terrytao.files.wordpress.com/2012/12/gsm-126-tao5-measure-book.pdf
Teaching methods
Lectures and exercise sessions.
Assessment methods
Written and oral exam.
A slightly different assessment method will be used for students who are especially active in their participation.
Teaching tools
Online tools and repository of course material.
Office hours
See the website of Nicola Arcozzi
SDGs
This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.