OVERVIEW

Course of the III year of Laurea Triennale in Mathematics; the course consists of two parts: complex analysis and functional analysis, both at introductory level.

AIMS AND CONTENT

LEARNING OUTCOMES

The aim is to give some basic tools in complex and functional analysis. Such tools will allow students to absorb some concepts and techniques fundamental for any direction of further study or job.

AIMS AND LEARNING OUTCOMES

Students will be able to solve simple problems and to follow more advanced studies in complex and functional analysis.

PREREQUISITES

Analysis, Geometry and Algebra courses from the first two years of Laurea Triennale in Mathematics.

TEACHING METHODS

The classical method: lectures and exercises using the blackboard; written (exercises) and oral (theory and exercises) examination. Special importance is given to exercises and consequently to the written part of the exam.

SYLLABUS/CONTENT

Complex Analysis: power series and analytic functions; complex differentiation and holomorpgic functions; complex integration, Cauchy's theorem and primitives; classical consequences of Cauchy's theorem; singularities, residue theorem and applications.

Functional Analysis: normed spaces; linear operators; scalar products; Hilbert spaces and orthonormal bases; projection theorem and Riesz representation theorem; study of important examples: the space L^2 and Fourier series.

RECOMMENDED READING/BIBLIOGRAPHY

V.Villani - Funzioni di Una Variabile Complessa - Edizioni Scientifiche Genova 1971.

I.Stewart, D.Tall - Complex Analysis, 2nd ed. - Cambridge U. P. 2018.

H.Cartan - Elementary Theory of Analytic Functions of One or Several Variables - Dover Publ. 1995.

A.I.Markushevich - Theory of Functions of a Complex Variable, parts I--III - A.M.S. Chelsea Publishing 2005.

W.Rudin - Analisi Reale e Complessa - Bollati Boringhieri 1978.

M.Reed, B.Simon - Functional analysis - Academic Press 1972.

E.M.Stein, R.Shakarchi - Real Analysis - Princeton U. P. 2005.

TEACHERS AND EXAM BOARD

Exam Board

ALBERTO PERELLI (President)

GIOVANNI ALBERTI

SANDRO BETTIN (President Substitute)

LESSONS

LESSONS START

When lessons of the III year start.

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written and oral examination.

Students with DSA certification ("specific learning disabilities"), disability or other special educational needs are advised to contact the teacher at the beginning of the course to agree on teaching and examination methods that, in compliance with the teaching objectives, take account of individual learning arrangements and provide appropriate compensatory tools.

ASSESSMENT METHODS

Evaluation of written and oral examination.

Exam schedule