Mathematics

ADRIANO PISANTE

GENERAL OBJECTIVES: to obtain a basic knowledge of function spaces of everyday use in Analysis, and of the most important techniques used in their study (Measure Theory, Distribution Theory, Harmonic Analysis).


SPECIFIC OBJECTIVES:

Knowledge and understanding: at the end of the course, the student will posses a running knowledge of the main function spaces used in Analysis and of the methods used in their study.

Applying knowledge and understanding: the student will be able to apply the many techniques learned in this course to several different areas, in particular to problems from the theory of Partial Differential Equations.

Critical and judgment skills: this course has a foundational charactr; its main purpose is precisely to deepen the understanding of some fundamental techniques of common use in Analysis.

Communication skills: the student will be able to fully understand a scientific text of high complexity and relate on the essential ideas contained in it.

Learning skills: the notions and techinques learned will give the student access to more advanced notions in Analysis.

GENERAL OBJECTIVES: to obtain a basic knowledge of function spaces of everyday use in Analysis, and of the most important techniques used in their study (Measure Theory, Distribution Theory, Harmonic Analysis).


SPECIFIC OBJECTIVES:

Knowledge and understanding: at the end of the course, the student will posses a running knowledge of the main function spaces used in Analysis and of the methods used in their study.

Applying knowledge and understanding: the student will be able to apply the many techniques learned in this course to several different areas, in particular to problems from the theory of Partial Differential Equations.

Critical and judgment skills: this course has a foundational charactr; its main purpose is precisely to deepen the understanding of some fundamental techniques of common use in Analysis.

Communication skills: the student will be able to fully understand a scientific text of high complexity and relate on the essential ideas contained in it.

Learning skills: the notions and techinques learned will give the student access to more advanced notions in Analysis.

Students are required to be familar with Advanced Calculus (Functions of Several Variables). A cursory knowledge of Measure Theory and Functional Analysis will be greatly helpful, although not strictly necessary.

A review of Measure Theory. A review of Functional Analysis. Lp spaces. Distribution theory. Sobolev spaces. Fourier transform.

1) Course notes (can be downloaded from the website of the course)
2) G.F.Folland, Real Analysis
3) H.Brezis, Functional Analysis
4) L.C.Evans, Partial Differential Equations
5) L.C.Evans and R.Gariepy, Measure Theory and Fine Properties of Functions

The web page for the course is available on the platform elearning by registering at the webpage https://elearning.uniroma1.it

The web page for the course is available on the platform elearning by registering at the webpage https://elearning.uniroma1.it

60% lectures, 40% supervised exercises.

Students are strongly encouraged to attend the classes

The goal of the exam is to assess the level of preparation through one written and one oral exam. The written exam has a duration of 2h.
To pass the exam a mark not less than 1i/30 is required. To get this, the student must show a sufficient knowledge of the simpler techinques and the most important arguments touched during the course.
To get full marks, 30/30 e lode, the student must show an excellent knowledge of all topics covered during the course.