Mathematics II

Matrices (basic operations, matrix product, rank, determinant, eigenvalues, eigenvectors, linear transformations). Systems of linear equations (Gauss elimination, Cramer's rule).

Vectors (basic operations, scalar product, vector product, scalar triple product, analytic geometry). Function series (power series, Taylor series, Fourier series). Functions of two and more variables (partial derivatives, chain rule, extrema, conditional extrema). Ordinary differential equations (ODE) of the first order (with separable variables, linear, first integral). Linear ODE of higher orders (with constant coefficients, Euler's equation). Linear systems of ODEs, linearly independent solutions.

To present and upgrade basic mathematical concepts, procedures, and laws, and to deepen their understanding. To develop analytical thinking, careful and exact mathematical reasoning as well as other building blocks of science/mathematics/engineering literacy. To become familiar with the software for symbolic computations (e.g., Mathematica).

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