ANALISI MATEMATICA III

Degree course: 
Corso di Second cycle degree in Physics
Academic year when starting the degree: 
2014/2015
Year: 
1
Academic year in which the course will be held: 
2014/2015
Course type: 
Supplementary compulsory subjects
Credits: 
6
Period: 
First Semester
Standard lectures hours: 
60
Detail of lecture’s hours: 
Lesson (60 hours)
Requirements: 

Mathematical Analysis 1, Mathematical Analysis 2 and Linear Algebra and Geometry.

Assessment: 
Voto Finale

The goal of the course is deepen the knowledge of classical analysis and to give an introduction to real and functional analysis.
Students will acquire a working knowledge of the methods of advanced analysis. They will know statements and proofs of the main theorems, and will be able to solve exercises, even of theoretical nature, about the topics dealt with in the course. They will have learned a number of techniques of proof, which they will be able to use to prove results related to those described in class.

Convergence of sequences and series of functions. Power and Taylor’s series. Fundamentals of Banach and Hilbert spaces. Lp spaces and their properties. Differential 1-forms in Rn. Fourier series.
Lectures: 56 hours
Exercise sessions: 12 hours

W. Rudin, Principles of Mathematical Analysis, Mc Graw Hill.
W. Rudin, Real and Complex Analysis, Mc Graw Hill.
E. Giusti, Analisi Matematica 2, Boringhieri
E. Giusti, Complementi di Analisi Matematica 2, Boringhieri
Written examination on exercises, followed by an oral examination consisting in the discussion of the written test and in answering questions on the theory. The access to the oral part is conditioned to having obtained at least 14/30 in the written part.

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