Mathematics

Activity type

Formazione Teorica

SSD

MAT/05

Year

3rd year

Semester

2nd semester

CFU

3

Hours distribution

24 classroom hours

Lecturers

RICCARDO SALVATI MANNI

Activity type

Formazione Teorica

SSD

MAT/03

Year

3rd year

Semester

2nd semester

CFU

3

Hours distribution

24 classroom hours

Lecturers

RICCARDO SALVATI MANNI

General objectives: to acquire basic knowledge in the theory of a complex variable.

Specific objectives:

Knowledge and understanding: at the end of the course the student will have acquired the basic notions and results related to holomorphic and meromorphic functions, the problem of the calculation of residues and numerous applications, to the analysis of infinite products and some fundamental functions.

Apply knowledge and understanding: at the end of the course the student will be able to solve simple problems that require the use of techniques related to the complex variable; will be able to calculate improper integrals and to study some special examples of holomorphic and meromorphic functions.

Critical and judgmental skills: the student will have the bases to analyze the similarities and relationships between the topics covered and topics of analysis (acquired in the course of Analysis II) or geometry (which can be acquired in the course of Geometry II); will also acquire the tools that have historically led to the solution of classical problems.

Communication skills: ability to expose the contents in the oral part of the assessment and in any theoretical questions present in the written test.

Learning skills: the acquired knowledge will allow a study, individual or given in an LM course, related to more specialized aspects of the complex variable and the analytic number theory.

Module:
rudiments of complex Analysis


Module:
To be able to use the complex variable

Module:
Calculus in several variables, general topology


Module:
First part

Module:
Differential and complex calculus in the complex plane, Analytic functions, the Residue Theorem and applications.
Logarithm, complex n-th root. Construction of analytic functions


Module:
Gamma Function, infinite products, Elliptic functions

Module:
Rolf Busam , Eberhard Freitag: Complex Analysis


Module:
Rolf Busam , Eberhard Freitag: Complex Analysis

Module:
N/D
Module:
N/D

Module:
Classes with exercises


Module:
Lessons and exercises

Module:
in presence


Module:
In presence

Module:
To pass the exam, a grade of not less than 18/30 must be obtained. The student must
to demonstrate to have acquired a sufficient knowledge of the arguments of both
parts of the program and to be able to
carry out at least the simplest among the assigned exercises.
To achieve a score of 30/30 cum laude, the student must instead demonstrate
have acquired an excellent knowledge of all the topics covered during the course and
be able to link them in a logical and consistent way.


Module:
To pass the exam, a grade of not less than 18/30 must be obtained. The student must
to demonstrate to have acquired a sufficient knowledge of the arguments of both
parts of the program and to be able to
carry out at least the simplest among the assigned exercises.
To achieve a score of 30/30 cum laude, the student must instead demonstrate
have acquired an excellent knowledge of all the topics covered during the course and
be able to link them in a logical and consistent way.

Module:
See web page
https://www1.mat.uniroma1.it/people/salvati/


Module:
See web page
https://www1.mat.uniroma1.it/people/salvati/

Module:
N/D
Module:
N/D