
Course unit
FUNCTIONS OF SEVERAL COMPLEX VARIABLES
SCN1037792, A.A. 2019/20
Information concerning the students who enrolled in A.Y. 2019/20
ECTS: details
Type 
ScientificDisciplinary Sector 
Credits allocated 
Core courses 
MAT/05 
Mathematical Analysis 
6.0 
Course unit organization
Period 
First semester 
Year 
1st Year 
Teaching method 
frontal 
Type of hours 
Credits 
Teaching hours 
Hours of Individual study 
Shifts 
Practice 
3.0 
24 
51.0 
No turn 
Lecture 
3.0 
24 
51.0 
No turn 
Examination board
Examination board not defined
Prerequisites:

Integral and differential calculus in several variables. 
Target skills and knowledge:

Knowledge of the basic properties of holomorphic functions in several variables. In particular learning the techniques for dealing with such functions. 
Examination methods:

Oral exam 
Assessment criteria:

Knowledge of the topics exposed in class. 
Course unit contents:

1. Real and complex differentials
2. Cauchy formula on polydiscs
3. Subharmonic functions
4. Separate analytic functions
5. Analytic functions and convergent power series
6. Levi form and H. Lewy's extension theorem
7. Logarithmic Superharmonicity, Continuity principle, Propagation of holomorphic extendibility
8. Domains of holomorphy end pseudoconvex domains
9. L2 estimates and Neumann problem 
Planned learning activities and teaching methods:

lectures and tutorials 
Textbooks (and optional supplementary readings) 

Giuseppe Zampieri, Complex analysis and CR Geometry. : American Math. Soc., 2008.


