Complex analysis: Cauchy theorem, Taylor and Laurent series, calculus of residues. Laplace transform. Fourier series and Fourier transform. Introduction to functional analysis: linear operators on Hilbert spaces.
G. Cosenza, "Metodi Matematici della Fisica", Bollati Boringhieri.
G. De Marco, "Analisi 2", decibel Zanichelli.
G. Fano, "Metodi matematici della meccanica quantistica", Zanichelli.
O.Luongo e S.Mancini, "Introduzione ai Metodi matematici delle Scienze fisiche".
Furthe didactic material will be available on the moodlle web site of the course.
Learning Objectives
Knowledge acquired:
Mathematical methods for solving problems of mathematical physics and mathematical formalism of Quantum Mechanics.
Skills acquired (at the end of the course):
Calculus of integrals with the residue method, Fourier and Laplace transforms, solution of differential equations.
Prerequisites
Courses required: Mathematical analysis I, Geometry.
Teaching Methods
Exposition on the blackboard and projection of slides
Further information
CFU: 6
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150
Contact hours for: Lectures (hours): 52
Type of Assessment
Written exam (test of ability in solving problems) duration 2 hours;
oral exam (test of the degree of comprehension of conceptual aspects of the course) duration 45 minutes.
Course program
Complex analysis: holomorphy, integration, Cauchy theorem, Taylor and Laurent series, calculus of residues, Jordan lemma.
Fourier series. Fourier transform in L1 and L2.
Laplace transforms.
Hilbert spaces, linear operators on Hilbert spaces, spectrum of operators.