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Lecturer(s)
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Peška Patrik, RNDr. Ph.D.
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Mikeš Josef, prof. RNDr. DrSc.
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Course content
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1. Vector functions. | 2. Methods of definitions of curves. | 3. Length of a curve, natural parameter. | 4. Frenet's reper and equations. | 5. Contact of curves, osculation circle. 6. Methods of definitions of surfaces. 7. Tangent plane and normal of surface. | 8. First and second fundamental forms of the surface. Meussnier theorem. 9. Curvature of surface. Euler's formula. | 10. Gauss and Weiengarten formulas, Egregium theorem. 11. Special curves on the surface. 12. Special surfaces. 13. Differentiaable manifolds, affine connection, Riemann manifolds.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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1. Knowledge Recall properties of important curves (main, asymptotic, geodesic) on surfaces and the role of geodesics for mechanics.
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Prerequisites
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unspecified
KAG/AGN
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Assessment methods and criteria
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unspecified
Credit: the student has to pass two written tests (i.e. to obtain at least half of possible points in each test). Exam: the student has to understand the subject and be able to use the theory in applications.
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Recommended literature
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Budinský B., Kepr B. (1970). Základy diferenciální geometrie s technickými aplikacemi. SNTL Praha.
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Doupovec, M. (1999). Diferenciální geometrie a tenzorový počet. VUT Brno.
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Gray A. (1994). Differential geometry. CRC Press Inc.
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J. Mikeš, E. Stepanova, A. Vanžurová et al. (2015). Differential geometry of special mappings. UP Olomouc.
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J. Mikeš, M. Sochor. (2013). Diferenciální geometrie ploch v úlohách. UP OLomouc.
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Metelka, J. (1969). Diferenciální geometrie. SPN Praha.
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