# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2016/2017
Belonging course:
Course of Master's Degree Programme on INFORMATION AND COMMUNICATION TECHNOLOGY ENGINEERING
Location:
Napoli
Disciplinary sector:
MATHEMATICAL ANALYSIS (MAT/05)
Credits:
9
Year of study:
1
Teachers:
Dott. FEO Filomena
Cycle:
First Semester
Hours of front activity:
72

### Course description

The aim of the course is the knowledge and understanding of basic concepts of complex analysis, Laplace transform, Fourier transform and distribution.

The student has to

- Show knowledge and understanding of basic concepts.

- Understand and explain the meaning of theorem using mathematical notation and language;

- Demonstrate skill in mathematical reasoning, manipulation and calculation

- Be able to apply his/her knowledge and understanding in different contexts;

The key skills expected are

- Ability to construct and develop logical mathematical arguments with clear identification of assumptions and conclusions . The student has to read and master a topic and demonstrate mastery in a reasoned written and/or verbal report

- Ability to present mathematical arguments and the conclusions from them with clarity and accuracy and in forms that are suitable for the audiences being addressed, both orally and in writing

- Learning skills to undertake further studies with some autonomy

### Prerequisites

The student has to know and to be able to use the tools introduced in Calculus I and II, especially differential calculus and integral calculus

### Syllabus

Preliminaries ( 7 hours of Lectures +1 hour of Exercise session)

Complex functions, topology of complex field, sequences and series.

Complex analysis (20 hours of Lectures + 4 hours of Exercise session)

Cauchy integral theorem, analyticity of holomorphic functions, Laurent series, study of isolated singularities, Residue theorems and application to calculus of real integrals. Different notion of integrability.

Functional analysis and Fourier series (15 hours of Lectures + 3 hours of Exercise session)

Metric spaces, Banach spaces, Hilbert spaces, Fourier series in an Hilbert space. Pointwise convergence of the Trigonometric Fourier serie.

Laplace transform (6 hours of lectures+ 1 hour of Exercise session)

Definition of Laplace transform and main properties. Application to ODE.

Fourier transform (6 hours of Lectures + 1 hour of Exercise session)

Definition of Fourier transform and main properties.

Distribution(5 hours of Lectures + 1 hour of Exercise session)

Definition of distribution, main properties and Fourier transform of a distribution.

A short introduction to PDE (3 hours of Lectures)

### Textbooks

G.C. Barozzi, Matematica per l`Ingegneria dell`Informazione, Zanichelli.

S. Abenda - S. Matarasso, Metodi Matematici, Editrice Esculapio. G.C. Barozzi, Matematica per l`Ingegneria dell`Informazione, Zanichelli. M. Codegone, Metodi Matematici per l`Ingegneria, Zanichelli.

Moreover see
http://edi.uniparthenope.it/course/view.php?id=41
for examples of test and of exercises.

### Learning assessment

The final exam tests the achievement of the training objectives.

The final examination consists of two parts:

- a written test to verify the knowledge and understanding of arguments. The test takes 2 hours and student cannot use any books, pc or smartphones. He has to pass the text in order to move on the next step.
-a discussion about some connections and comparison between different considered arguments.

The final score refers to both parts.