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 integration for functions of two and three variables, the theory of differential forms, the Fourier's series 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) Integration on R^2 and R^3, path and surface integration of differential forms. 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 on R^2 and R^3. Integration of differential forms. Gradient, divergence, curl and their properties.

2) Series of functions, Fourier series and applications.

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

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

Evaluation of integrals on R^2 and R^3. Integration of differential forms. Calculus of gradient, divergence, curl. Fourier series expansions and applications to differential equations. Integration on the complex plane and evaluation of residues with application to improper integrals.

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, numerical series, series of functions, power series and ordinary differential equations.

TEACHING METHODS

Both theory and exercises are presented by the teacher in the usual way. Moreover some tutorial exercitations can be carried out during the semester.

SYLLABUS/CONTENT

First part: Integrals on R^2 and R^3. Curves and surfaces in R^3. Vector analysis: differential forms and path integrals, closed and exact differential forms, gradient, curl, divergence. Stokes Theorem.

Second part: Series of functions, Fourier series.

Third part: Functions of a complex variable. Analytic functions and Taylor series. Residue theorem and application to improper integrals.

RECOMMENDED READING/BIBLIOGRAPHY

• O. Caligaris, P. Oliva - Analisi matematica 2 - E.C.I.G.
• O. Caligaris, P. Oliva - Complementi di analisi matematica
• W. Rudin - Real and Complex Analysis - McGraw-Hill 1970
• N. Fusco, P. Marcellini, C. Sbordone - Lezioni di analisi matematica 2 - Zanichelli (2020)
• M. Chicco, F. Ferro - Esercizi di Analisi matematica II - E.C.I.G. 

TEACHERS AND EXAM BOARD

Exam Board

ADA ARUFFO (President)

CLAUDIO ESTATICO

LAURA BURLANDO (President Substitute)

LESSONS

LESSONS START

https://corsi.unige.it/9273/p/studenti-orario

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

If the University decides to return to usual teaching: written and oral tests. Oral test, which students can access whatever the outcome of written test, has to be taken in the same exam session of written test.

Otherwise, if, due to the COVID emergency, restrictions remain and if will not be possible to return to the fact that the exams for all students are in presence, as the University allows the exams for some students is online, the exam will be held only in oral form, the exam sessions will become seven and the relative dates will be those initially fixed for the January written test, for the January oral test, for the February written test, for the June written test, for the June oral test, for the July written test and for the September written test.

ASSESSMENT METHODS

The written examination consists in some exercises about the topics covered in this course. In this test the ability to apply theoretical results in concrete situations is evaluated.

The test lasts two hours and it is possible to consult the notes and textbooks.

In the oral exam a discussion of the written examination is done; moreover some questions are asked on the course content and/or about the solution of some exercises about the topics covered in this course. In such way they are assessed the understanding, the knowledge of the concepts, and the skills in using them, acquired by the students.

Exam schedule

FURTHER INFORMATION

Attendance is recommended.

Students are suggested to enroll in AulaWeb, in order to be able to get further information by the teachers about the course.