OVERVIEW

This module deals with some issues of Mathematical Analysis with the aim to complete the basic learning and introduce some theoretical tools used in engineering science.The main topics concern with the theory of vector fields, the Fourier's analysis and the functions of a complex variable.

AIMS AND CONTENT

LEARNING OUTCOMES

The module aims to introduce the basic methods for the following topics in Mathematical Analysis: 1) Path and surface integration for vector fields, differential operators. 2) Fourier series and applications. 3) Functions of one complex variable, integration, computation of residues and applications.

AIMS AND LEARNING OUTCOMES

This module aims to provide the student with the knowledge of the following mathematical conceps:

1) Integration of differential forms. Vector flux, divergence, curl and their properties for vector fields.

2) Orthogonal functions, Fourier series and applications.

3) Functions of one complex variable and integration on a path in the complex plane. Computation of residues, Fourier and Laplace transforms and applications.

The main learning outcomes consist of technical skills about the following issues:

Evaluation of maxima and minima under constrains. Integration of differential forms. Vector calculus and use of differential operators. Fourier series expansions and applications to differential equations. Integration on the complex plane and evaluation of residues. Applications of Fourier and Laplace transforms.

PREREQUISITES

Basic knowledge on linear algebra and differential calculus are required as prerequisites. In particular, the student must be familiar with the analysis of functions of one and more variables, series  of functions, and ordinary differential equations.

TEACHING METHODS

Lectures on the theoretical contents, examples and exercises.

SYLLABUS/CONTENT

First part:  Maxima and minima with constraints. Vector analysis: Differential forms and path integrals, vector fields, circulation, flux, divergence and Stokes theorems.

Second part: Fourier series and applications

Third part: Functions of a complex variable. Analytic functions and McLaurin series. Residue theorem and application to improper integrals. Fourier Transform and applications. Laplace transform.

RECOMMENDED READING/BIBLIOGRAPHY

• Lecture notes by the teacher (available on Aulaweb)
• L. Recine, M. Romeo,  Esercizi di Analisi Matematica (vol 2, Funzioni di più variabili ed equazioni differenziali), 2^ edizione, Maggioli (2013)
• G.C. Barozzi, Matematica per l’Ingegneria dell’informazione, Zanichelli 2004.
• G. B. Folland, Fourier Analysis and its applications, Wadsworth, Belmont, 1992.
• J.E. Marsden and M.J. Hoffman , Basic  Complex Analysis, Freeman and Co., New York, 1987. 

TEACHERS AND EXAM BOARD

Exam Board

MAURIZIO ROMEO (President)

CLAUDIO ESTATICO

ANGELO MORRO

LESSONS

LESSONS START

September, 17, 2018

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

A written test on  tecnical skills (the required result must be greater or equal to 18/30). This is a prerequisite for an oral exam concerning theoretical issues.

ASSESSMENT METHODS

The written test is intended to verify technical skills about the following points: 1) Computation of maxima and minima with constraint, 2) Computation of field lines or potentials for vector fields, 3) Fourier series expansion of a periodic function and its application to  numeric series, 4) Evaluation of improper integrals by residues or derivation of Laplace transforms

The objective of the spoken exam is to verify the student's knowledge about theoretical concepts. The student is required to state and prove theorems, showing to be aware of formulas and notations adopted.

Exam schedule