Complex analysis: Cauchy theorem, Taylor and Laurent series, calculus of residues, Jordan lemma. Fourier and Laplace transforms. Introduction to the theory of distributions, Fourier transform of distributions. Introduction to functional analysis: operators on Hilbert spaces
Notes by Prof. Daniele Dominici (http://theory.fi.infn.it/dominici/metodi.html), by Prof. Giovanni Martucci and books in their bibliography.
G. Cosenza, Metodi Matematici della Fisica, Bollati Boringhieri
Problems: M.L. Krasnov, A.I. Kiselev e G.I. Makarenko, Funzioni di variabile complessa e loro applicazioni, MIR 1981.
R. Shakarchi, Problems and solutions for complex analysis, Springer 1999.
Collection of past written examinations available in the Library office.
Learning Objectives
Knowledge acquired:
Mathematical methods for solving problems of mathematical physics and mathematical formalism of Quantum Mechanics
Competence acquired
Complex Analysis and Functional Analysis.
Skills acquired (at the end of the course):
Calculus of integrals with the residuous, Fourier and Laplace transforms, use of distributions, solution of differential equations.
Prerequisites
Courses required: Mathematical analysis I, Geometry
Recommended courses:
Teaching Methods
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
Further information
Office hours: Wednesday 15.00-17.00
Website:
Type of Assessment
Written and oral exam
Course program
Complex analysis: Cauchy theorem, Taylor and Laurent series, calculus of residues, Jordan lemma. Fourier and Laplace transforms. Introduction to the theory of distributions, Fourier transform of distributions. Introduction to functional analysis: operators on Hilbert spaces.