Course title:
Mathematical physics practicum
2023/2024
Programme:
Physics, First Cycle
Orientation:
Astronomy
Year:
3 year
Semester:
first
Kind:
optional
ECTS:
6
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 1. semester:
Lectures
6
Seminar
0
Tutorial
0
Lab
0
Content (Syllabus outline)
Computing and plotting functions: power and asymptotic series, Pade approximations, chain fractions; plotting vector fields.
Eigenvalues and eigenvectors of a tensor.
Harmonic analysis: Fast Fourier transform (FFT), correlation function.
(Systems of) simple (ordinary) differential equations: initial-value problems, stiff systems, boundary-value problems.
Partial differential equations: 1-D wave and diffusion equation, Fourier method, finite-difference method (discretization), Galerkin method.
Readings
S. Širca, M. Horvat, Računske metode za fizike, DMFA Ljubljana 2011.
S. Širca, M. Horvat, Computational methods for physicists, Springer-Verlag 2012.
W. H. Press et al., Numerical Recipes. Cambridge University Press 2007.
I. Kuščer, A. Kodre, Matematika v fiziki in tehniki. DMFA Ljubljana 1994.
Objectives and competences
The student acquires experience in the application of mathematical tools for the numerical and symbolic analysis and for the visualization of data.
Intended learning outcomes
Knowledge and understanding
Understanding of the execution of computational procedures and the choice of the computational method.
Application
The skill of quantitative evaluation of concrete physics and technical problems.
Reflection
Interpretation of numerical results.
Transferrable skills
The skill of the numerical solution of the project. The skill of reporting about the computational project. Application of computer graphics for data visualization. Managing programming languages and computational tools.
Learning and teaching methods
Weekly projects, live computer presentations, consultations.
Assessment
The grade is given according to the grades of individual projects (12 weekly problems).
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)
Lecturer's references
[1] S. Širca, M. Horvat, Računske metode za fizike, DMFA, Ljubljana 2011. (also available as S. Širca, M. Horvat, Computational Methods for Physicists, Springer-Verlag, Berlin 2013). [2] O. Gayou, S. Širca et al., Phys. Rev. Lett. 88 (2002) 092301. [3] J. J. Kelly, S. Širca et al., Phys. Rev. Lett. 95 (2005) 102001. [4] R. Subedi, S. Širca et al., Science 320 (2008) 1476. [5] S. Širca, Few-Body Systems 47 (2009) 39.
