Infinite series- numerical and functional, criteria of convergency. Power and Taylor series. Integration and derivative of power series, application for intagration of functions the primitive functions of which is not elementary. Solution of differential equations by means of power series. Elementary functions of complex variables, Euler formulas. The concept of a real and complex harmonic function, trigonometrical polynomials. Fourier trigonometrical polynomial, physical meaning. Fourier trigonometriacal series, conditions of convergency and regularity. 1-dimensional equation of heat conduction and its solution by means of Fourier series. Various inital and boundary conditions (Dirichlet, Neumann).
Fourier transform and its physical meaning. Vocabulary of the Fourier transform and the convolution theorem. Dirac function and its definition as a distribution. Applications for signals with a periodical component. Information on applications in the spectroscopy (apodizing curves, deconvolution methods, distinctevness). Discrete and fast Fourier transformation.
Linear and quasilinear 1-st order partial differential equations and their systems, physical motivation. 2-nd order partial differential equations, the potencial, wave and diffusion (heat flux) equation. Dirichlet, Neumann a Newton boundary conditions and physical examples. Numerical methods for their solution - the method of Ritz, Galerkin and the finite elements method.
Tensors and tensor fields, a medium for an expression of a linear dependence of a scalar or vector entity on other vector entities (tensor of polarization, torsion, strain, deformation, tensor of electromagnetic field). Tensor form of physical laws. Informatively metric tensor, general relativity timespace. The concept of a smooth manifold operations on tensor fields induced by the metric tensor, covariant derivative, Hamilton and d'Alembert operator.
Vector and euclidian spaces, fundamental topological concepts, giving of a curve and a surface, fundamental concepts of classical differential geometry, basic information on some kinds of curvatures, tensors. Introduction to the theory of partial differential equations (PDE],
some kinds of PDE's and their solutions, (Schrödinger equation), elements of variational calculus and fractal theory.