Upon completing the course, students learn the following skills. They are able to
- explain mathematical problems and concepts as well as mathematical proof processes (k2);
- independently develop mathematical solutions and proofs of mathematical problems in the field of analysis of many variables (k3);
- apply concepts and problem-solving strategies to new and unfamiliar questions, selecting and using appropriate mathematical methods (k3/k4);
- present their solutions to the group and discuss different approaches (k3/k4).
|
During the course, students acquire knowledge in the analysis of several variables:
- multidimensional differentiation (partial derivative, Fréchet derivative), Taylor formula;
- multidimensional Riemann integral;
- volumes, scalar integration over curves and surfaces;
- integration of 1- and 2-forms over curves and surfaces;
- exterior derivative (gradient, curl, divergence);
- Green’s theorem, Stokes’ theorem, and Gauss’ theorem;
- differentiation and integration of complex functions, Cauchy's integral theorem and integral formula, residue theorem.
|
