Real Analysis

C.L. in Matematica

Universita' di Milano - Anno Academico 2017/2018

Proff. K. R. Payne e  L. Vesely


 Preliminary syllabus (programma preliminare) (file rtf) 

Final detailed syllabus (programma d'esame) (file .pdf) (Available towards the end of the course)


ANNOUNCEMENTS: 

1.      Homework Results.

a.      HW1

b.      HW2

c.       HW3 (version of 28 February)

2.      Prossime prove orali:

a.      Marted́ 19 giugno: 9.30-14.30 in Aula 6 (Studenti che intendono presentarsi sono pregati di confermare la presenza entro Domenica 17 giugno tramite e-mail al Prof. Payne)

b.      Marted́ 17 luglio: 9.30-14.30 in Aula 6 (Studenti che intendono presentarsi sono pregati di confermare la presenza entro Domenica 15 luglio tramite e-mail al Prof. Payne)

 

 

 

 

 

 


Office hours (ricevimento studenti):   Monday and Thursday 11.30 – 12.30 and by appointment.


Teaching materials:

Corse notes:  These will be updated during the course, but for now here is the link to an old version that covers the first two chapters of the course.

1.      Differentiation and Integration + Lp spaces (K. Payne, in Italian)

2.      Hilbert Spaces (K. Payne, in English)

a.      Lectures 16 & 17 (Hilbert spaces, orthogonality, the Projection Theorem, duality, Riesz Representation Theorem, Lax Milgram Theorem)

b.      Lectures 18 & 19 (Orthonornal systems, orthonormal bases, separablity, bounded linear operators, adjoint operators, compact operators)

c.       Lectures 20 & 21 (The Spectral Theorem, pointwise convergence of Fourier series, summability kernels, Riemann-Lebesgue Lemma)

 

Homework assignments   

1.      Homework N.1 – due date is Thursday, November 9.

2.      Homework N.2 – due date is Tuesday, December 19. (New Version of December 11)

3.      Homework N.3 – due date is Monday, January 22.

 

 

 

    

Old exercizes from past years      Raccolta di Esercizi di Analisi Reale, Parte I  (in Italian)