Mathematical methods in physics

A.Y. 2015/2016
7
Max ECTS
60
Overall hours
SSD
FIS/02
Language
Italian
Learning objectives
Il corso ha carattere introduttivo e mira a fornire conoscenze
di base di metodo e rigore matematico, tecniche utili e
qualche applicazione negli ambiti: Analisi complessa, Spazi
di Hilbert e Operatori Lineari, Serie e Integrali di Fourier e
Laplace, Distribuzioni.
Expected learning outcomes
Undefined
Course syllabus and organization

CORSO A

Responsible
Lesson period
Second semester
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 7
Practicals: 20 hours
Lessons: 40 hours

CORSO B

Responsible
Lesson period
Second semester
Course syllabus
PROGRAM:
1) Functions of a complex variable
- Introduction to complex numbers
- Complex numbers in physics
- Analytic functions
- Domain
- Cauchy-Rieman conditions
- Laplace equation
- Singularities
- Polydromy
2) Integration of function of complex variable
- Line integrals
- Cauchy theorem
- Cauchy integral formula
- Jordan lemma
- Dispersion relations
3) Integral and series representations
- Convergency
- Taylor and Laurent series
- Integrals with residuals
- Analytic continuation
- Laplace transform
- Fourier transform
4) Linear spaces
- Abstract linear spaces
- Linear functionals
- Distributions
- Linear operators


C. Bernardini. O. Ragnisco, P. M. Santini
Metodi Matematici della Fisica. Carocci Editore
FIS/02 - THEORETICAL PHYSICS, MATHEMATICAL MODELS AND METHODS - University credits: 7
Practicals: 20 hours
Lessons: 40 hours
Professors: Raciti Mario, Zapperi Stefano
Professor(s)
Reception:
Please contact me by email
Reception:
11-12 Wednesday
zoom (send email for an appointment)