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Mathematics IV
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | English |
| Code | 310-3141/03 |
| Abbreviation | MIV |
| Course title | Mathematics IV |
| Credits | 5 |
| Coordinating department | Department of Mathematics and Descriptive Geometry |
| Course coordinator | prof. RNDr. Radek Kučera, Ph.D. |
Subject syllabus
1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions.
2 Euler method for homogeneous systems of n equations for n functions.
3 Variation of constants.
4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2.
5 Transformation - polar coordinates, geometrical and physical applications.
6 Three-dimensional integrals on coordinate cube, on bounded subset of R3.
7 Transformation - cylindrical and spherical coordinates, geometrical and physical applications.
8 Vector analysis, gradient.
9 Divergence, rotation.
10 Line integral of the first and of the second kind.
11 Green´s theorem, potential.
12 Geometrical and physical applications.
13 Surface integral of the first and of the second kind.
14 Stokes and Gauss-Ostrogradski theorem.
2 Euler method for homogeneous systems of n equations for n functions.
3 Variation of constants.
4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2.
5 Transformation - polar coordinates, geometrical and physical applications.
6 Three-dimensional integrals on coordinate cube, on bounded subset of R3.
7 Transformation - cylindrical and spherical coordinates, geometrical and physical applications.
8 Vector analysis, gradient.
9 Divergence, rotation.
10 Line integral of the first and of the second kind.
11 Green´s theorem, potential.
12 Geometrical and physical applications.
13 Surface integral of the first and of the second kind.
14 Stokes and Gauss-Ostrogradski theorem.