The aim of the course is to introduce to students mathematical methods and concepts that play an important role in some branches of advanced physics (e.g. electrodynamics, quantum mechanics) in more detail than taught in general mathematics. The focus is not on rigorous proofs of theorems, but on their illustration and applications to practical problems.

 

Topics (physical applications will be presented for the topics that overlap with the subjects specified in the prerequisites): Cylindrical, spherical coordinate systems, derivatives in them, the Laplace and Poisson equation, wave equation. Special functions and orthogonal functions with physical applications: Legendre polynomials, spherical harmonics, Bessel functions, Chebyshev polynomials. Physical applications of linear operators, similarity transformation. Distributions: their concepts, Dirac delta, their operations (derivation, convolution, Fourier and Laplace transforms), their use in solving differential equations, Green's function. Basics of complex analysis and some basic  applications.