96756 - Advanced Mathematical Analysus

Academic Year 2021/2022

  • 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