Mathematical physics I

• understanding mathematical description of physical problems using ordinary differential equations (ODEs);

• mastering construction of mathematical models of physical systems.

Analysis I

1. Basic concepts. Description of physical systems using ordinary differential equations (ODEs). Initial value problem. Boundary value problem. ODE solution. Existence and uniqueness of solutions.

2. First order ODEs. Separable ODEs. Exact ODEs. Integrating factors. Linear ODEs. Bernoulli's equation.

3. Second order ODEs. Physical examples of 2nd order ODEs. Harmonic oscillator. Electric circuits. Systems of ODEs as models.

4. Solution methods for 2nd order ODEs. Solutions using Laplace transforms. Series solutions. Special functions. Bessel functions. Legendre functions. Orthogonal functions.

5. Scalar and vector fields. Use of differential operators grad, div, curl and of integral theorems.

Students will learn:

• how to formulate physical problems using ordinary differential equations (ODEs);

• how to build and study mathematical models of physical systems using methods of solution of ODEs and systems of ODEs.

Basic:

E. Kreyszig, Advanced engineering mathematics, Wiley (2006). Catalogue E-version

Additional:

• L. Elsgolts, Differential equations and the calculus of variations, U.Press of Pacific (2004). Catalogue E-version
• T. Chow, Mathematical methods for physicists: a concise introduction, Cambridge (2000). Catalogue E-version
• G. Arfken, H. Weber, F. Harris, Mathematical methods for physicists, Elsevier (2012). Catalogue E-version
• I. Kuščer, A. Kodre, Matematika v fiziki in tehniki, DMFA, Ljubljana (2006). Catalogue

• completed homework
• written exam
• oral exam

Dr. Sergey Vorobyev je izredni profesor za področje fizike na Univerzi v Novi Gorici. Dr. Sergey Vorobyev is associate professor of physics at the University of Nova Gorica.

Njegova raziskovalna dejavnost je povezana z eksperimentalno fiziko kozmičnih žarkov in astronomijo gama žarkov zelo visokih energij.
Izbrane objave / selected publications:
MERTEN, L., VOROBIOV, S., et al., Scrutinizing FR 0 radio galaxies as ultra-high-energy cosmic ray source candidates. Astroparticle Physics, ISSN 0927-6505, 2021, v. 128, 1-22.
[COBISS.SI-ID 50457091].

Pierre Auger Collaboration, AAB, A., VOROBIOV, Serguei, et al., Observation of a large-scale anisotropy in the arrival directions of cosmic rays above 8×1018 eV. Science, ISSN 0036- 8075, sep. 2017, vol. 357, iss. 6357, str. 1266-1270, ilustr., doi: 10.1126/science.aan4338.
[COBISS.SI-ID 4921595].
SCHWANKE, U., VOROBIOV, Serguei, et al., A versatile digital camera trigger for telescopes in the Cherenkov Telescope Array. Nuclear instruments and methods in physics research. Section A, ISSN 0168-9002, 2015, vol. 782, str. 92-103, doi: 10.1016/j.nima.2015.01.096.
[COBISS.SI-ID 3758075].
CTA Consortium, ACTIS, M., VOROBIOV, Serguei, et al. Design concepts for the Cherenkov Telescope Array CTA : an advanced facility for ground-based high-energy gamma-ray astronomy. Experimental astronomy, Astrophysics and space science, ISSN 0922-6435, 2013, vol. 32, no. 3, str. 193, doi: 10.1007/s10686-011-9247-0. [COBISS.SI-ID 3234555].
VOROBIOV, Serguei, et al., NECTAr : new electronics for the Cherenkov Telescope Array. Nuclear instruments and methods in physics research A, ISSN 0168-9002, vol. 639, no. 1, 2011, str. 62, doi: 10.1016/j.nima.2010.08.112. [COBISS.SI-ID 3233787].
H.E.S.S. Collaboration, ABRAMOWSKI, A., VOROBIOV, Serguei, et al. Search for a dark matter annihilation signal from the galactic center halo with H.E.S.S. Physical review letters, ISSN 0031-9007, 2011, vol. 106, 161301-1-161301-5, [COBISS.SI-ID 3232251].
VOROBIOV, Serguei, HUSSAIN, Mustafa, VEBERIČ, Darko. Studies of UHECR propagation in the galactic magnetic field. V: CAPDEVIELLE, Jean-Noël (ur.), ENGEL, Ralph (ur.), PATTISON, Bryan (ur.). ISVHECRI 2008 proceedings, Paris, France, 2008, (Nuclear physics B, Proceedings suppl., ISSN 0920-5632, v. 196, s. 203. [COBISS.SI-ID 1305083].
DJANNATI-ATAI, A., VOROBIOV, Serguei, et al. Detection of the BL Lac Object 1ES 1426+428 in the very high energy gamma-ray band by the CAT telescope from 1998- 2000. Astronomy & astrophysics, ISSN 0004-6361, 2002, let. 391, št. 3, str. L25-L28.
[COBISS.SI-ID 564731].