Mathematics III

Differential geometry (scalar and vector fields, curves, surfaces in three-dimensional Euclidean space, parametrization). Multiple integral (parameter-dependent integral, double and triple integral, application). Vector analysis (gradient, divergence, curl, nabla operator). Line and surface integrals of scalar and vector fields (Green’s theorem, divergence theorem of Gauss, Stokes’s theorem). Complex analysis (complex analytic functions, elementary complex functions, complex integration, Laurent series, theory of residues). 

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.