Upon completing the course, students learn the following skills. They are able to
- understand and explain basic concepts of the analysis of many variables (k1/k2);
- understand and apply mathematical methods and techniques in a precise and analytical way (k3);
- apply the principles of the analysis of many variables and transfer them to the context of physical problems (k3).
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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.
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