Vector calculus in curvilinear coordinates, Tensor analysis, Second order linear differential equations and special functions. Complex variable, Fourier transform, vector spaces, Dirac delta and generalized functions. Numerical methods: interpolation and curve fitting, Numerical Differentiation and Integration, basics of computational physics, Hartree Fock and Density Functional theory, Monte Carlo simulations.
Main Textbook: Mathematical Methods for Physicists, by: George B. Arfken, Hans J. Weber and Frank E. Harris; Elsevier, 7th Ed. (2012). Subsidiary Books: Mathematical Methods in the Physical Sciences by Mary L. Boas. Publisher: Wiley; 3rd edition (2005). Mathematical Methods for Physics and Engineering by: Riley, Hobson, S. J. Bence. Publisher: Cambridge University Press; 3rd edition (2006) Mathematics for physicists, by: P. Dennery and A. Krzywickl; Dover (1995) Mathematics handbook for science and engineering, Rade Lennart, Westergren Bertil, 5, [rev.] ed.: Lund: Studentlitteratur: 2004: 562 s. Boyce William E., Elementary Differential Equations and Boundary Value Problems, 11th Edition, John Wiley & Sons: 2017:704 sidor Jon Mathews and Robert Walker, Mathematical Methods of Physics, Benjamin/Cummings, Publishing Co.