Credit Points: 3
Vector and tensor algebra: definitions, representations of tensors, examples. Complex functions: definitions, singular points, the Cauchy theorem and applications, conformal maps and applications, expansions of integrals, the Cauchy integral, the Hilbert arc problem. Integral transforms: Fourier, Laplace, Mellin, Hankel and Hilbert, applications to ordinary differential equations (separation of variables) and partial differential equations. Fredholm and Volterra integral equations. Introduction to the calculus of variations.