Subjects

Your browser does not support JavaScript, or its support is disabled. Some features may not be available.

Selected Topics on Mathematics for Physicists - NMAF006

Title:	Vybrané partie z matematiky pro fyziky
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2018
Semester:	summer
E-Credits:	3
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	taught
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time

Guarantor:	doc. RNDr. Mirko Rokyta, CSc.
Classification:	Physics > Mathematics for Physicists
Comes under:	Doporučené přednášky 1/2

Opinion survey results Examination dates Schedule Noticeboard

Annotation -

Last update: doc. RNDr. Mirko Rokyta, CSc. (18.02.2013)

An introduction to functional analysis, operator theory and special functions for physicists. It is the sequel to the basic 5-semester course of mathematics for physicists.

Literature -

Last update: T_KMA (15.05.2008)

J. Lukeš: Zápisky z funkcionální analýzy, skriptum MFF UK, Karolinum, 1998

P. Čihák, M.Rokyta a kol.: Matematická analýza pro fyziky (V), skriptum MFF UK, Matfyzpress 2003

K. Najzar: Funkcionální analýza, skriptum MFF UK, SPN, 1981

Syllabus -

Last update: doc. RNDr. Mirko Rokyta, CSc. (07.05.2018)

1. Basic facts on operators
Banach and Hilbert spaces. Operators and functionals, linear and nonlinear. Boundedness, continuity. Operator norm. Von Neumann series.

2. An introduction to spectral analysis
Eigenvalues, spectrum, resolvent set, spectral radius.

3. Compact operators
Compact operators, spectrum.

4. Dual and adjoint operators
Duality, dual operatost, dual spaces, representation theorems. Adjoint and self-adjoint operator, Hermite operator, their spectrum. Eigenfunction bases.

5. Unbounded operators.
Unbounded operator, closed operator. Differential operators.

6. Special functions and polynomials
Bases in Hilbert space, polynomial bases. Recurrent formulas for orthogonal polynomials. Special functions: Legendre, Laguerre, Hermite polynomials, hypergeometric series.

7. Green functions for ODEs
Green function for boundary value problem for ODE and its construction.