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.
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.
Students will be able to solve simple problems and to follow more advanced studies in complex and functional analysis.
Analysis, Geometry and Algebra courses from the first two years of Laurea Triennale in Mathematics.
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.
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.
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.
Ricevimento: On appointment; take directly an appointment with the professor or write to perelli@dima.unige.it
ALBERTO PERELLI (President)
GIOVANNI ALBERTI
SANDRO BETTIN (President Substitute)
When lessons of the III year start.
Written and oral examination.
Evaluation of written and oral examination.
