Course title:

# Mathematical physics practicum

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.

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.

The student acquires experience in the application of mathematical tools for the numerical and symbolic analysis and for the visualization of data.

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.

Weekly projects, live computer presentations, consultations.

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)

[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.