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Mathematics IV
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | Czech |
| Code | 310-3141/04 |
| 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 linear differential equations with constant coefficients – matrix form, fundamental system, elimination method.
2. Euler’s method for solving systems of linear differential equations, method of variation of constants.
3. Double integral over a rectangle, over a general closed planar region.
4. Transformation to polar coordinates, geometric and physical meaning.
5. Triple integral over a rectangular box, over a general closed three-dimensional regular region.
6. Transformation to cylindrical and spherical coordinates, geometric and physical applications.
7. Theory of scalar and vector fields: scalar field and its gradient, directional derivative.
8. Vector function, vector field, its divergence and curl.
9. Line integral of the first and second kind, physical and geometric interpretation, basic properties.
10. Computation of line integrals, Green’s theorem, path independence.
11. Surface integral of the first and second kind, physical and geometric interpretation, basic properties.
12. Computation of surface integrals, Stokes’ theorem, Gauss–Ostrogradsky theorem.
13. Discussion and verification of knowledge.
2. Euler’s method for solving systems of linear differential equations, method of variation of constants.
3. Double integral over a rectangle, over a general closed planar region.
4. Transformation to polar coordinates, geometric and physical meaning.
5. Triple integral over a rectangular box, over a general closed three-dimensional regular region.
6. Transformation to cylindrical and spherical coordinates, geometric and physical applications.
7. Theory of scalar and vector fields: scalar field and its gradient, directional derivative.
8. Vector function, vector field, its divergence and curl.
9. Line integral of the first and second kind, physical and geometric interpretation, basic properties.
10. Computation of line integrals, Green’s theorem, path independence.
11. Surface integral of the first and second kind, physical and geometric interpretation, basic properties.
12. Computation of surface integrals, Stokes’ theorem, Gauss–Ostrogradsky theorem.
13. Discussion and verification of knowledge.