- Docente: Nicola Arcozzi
- Credits: 6
- SSD: MAT/05
- Language: Italian
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
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)
Local properties of differentiable functions (Open Mapping, Inverse
Mapping, Implicit Function...)
Local theory for systems of ODEs (flow of a vector field)
Differential forms and Stokes' Theorem
Elements of measure theory
Hilbert space/Fourier series
Distributions/Fourier transforms
Sobolev spaces
Readings/Bibliography
Walter Rudin, Principles of Mathematical Analysis, McGraw-Hill 1976
Walter Rudin, Real and Complex Analysis, McGraw-Hill 1986
Lecture notes
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