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Lecturer(s)
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Zouvalová Katarína, Ing. Ph.D.
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Course content
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gradient, directional derivative, higher order partial derivatives. Week 2: Fundamental notions of min/max theory in Rn; Week 3: Double integral, Fubini's theorem. Week 4: Change of variables in a double integrals, polar coordinates. Week 5: Triple integral, methods to computation. change of variables. Week 6: Vector fields, divergence and curl. Hamilton operator, potential. Week 7: Laplace operator, curves. Week 8: Path integrals of scalar fields. Week 9: Path integrals of vector fields, Week 10: Surfaces and parametrization Week 11: Surface integral of scalar fields. Week 12: Surface integral of vector fields. Week 13: Integration theorems of vector calculus
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Learning activities and teaching methods
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Seminar classes, Seminar, Practicum
- Contact hours
- 26 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Preparation for comprehensive test (10-40)
- 18 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/M1E and KMA/M2E. |
| Skills |
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| To differentiate and integrate the functions of one real variable. |
| To draw basic curves. |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| Students will be able to understand the basic problems of differential calculus in Rn, they will be able to work with scalar and vector functions of one and more variables, to understand basic tasks of integral calculus for scalar and vector functions and integral theorems. |
| Skills |
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| Students will be able to solve basic problems from differential calculus in Rn, will be able to work with scalar and vector functions of one and more variables, compute simple double and triple integrals including substitutional method, simple curve and surface integrals, including use of integral sentences. |
| Competences |
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| N/A |
| teaching methods |
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| Knowledge |
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| Seminar |
| Seminar classes |
| Skills |
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| Seminar |
| Seminar classes |
| Competences |
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| Seminar |
| Seminar classes |
| assessment methods |
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| Knowledge |
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| Test |
| Skills demonstration during practicum |
| Skills |
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| Test |
| Skills demonstration during practicum |
| Competences |
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| Test |
| Skills demonstration during practicum |
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Recommended literature
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J. Bouchala, O. Vlach. Křivkový a plošný integrál.
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J. Kuben, Š. Mayerová, P. Račková, P. Šarmanová. Diferenciální počet funkcí více proměnných.
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P. Vodstrčil, J. Bouchala. Integrální počet funkcí více proměnných.
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