Mathematics IV

Integral transformations (Fourier transformation, Laplace transformation). Special functions (Gamma function, Beta function, Bessel functions). Power series solution of differential equations (Legendre's and Bessel's diferential equation, orthogonal system of functions). Partial differential equations (wave equation, heat equation, Laplace equation, solving differential equations with Laplace's transformation). Calculus of variations (functional, Euler-Lagrange equation, engineering examples). The finite difference method. The finite element method. 

To upgrade the basic concepts of mathematical analysis, procedures, and laws. Further develop analytical thinking, careful and exact mathematical reasoning as well as other building blocks of science/mathematics/engineering literacy. To upgrade the knowledge of the software for symbolic computations (e.g., Mathematica).

Lectures, tutorials, laboratory tutorials and homework assignments. Collective analysis, interpretation, and solving of technical problems.