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Lecturer(s)
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Pirklová Petra, Mgr. Ph.D.
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Course content
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- Point and vector function of one variable. Limit and derivative of a point/vector function. Geometric interpretation of a point and vector function of one variable. - Curve and its parametric description. Change of parameter. Plane and space curves. - Tangent, natural trihedron. Length of an arc, natural parameter. - Torsion and flection, Frenet's formulas. - Circle of osculation, centre of curvature. Properties of evolvent and evolute. - Point and vector function of two variables. Partial derivatives. - Surface and its parametric description. Parametric description of a curve on a surface. - Tangent plane and normal. - The first fundamental form of a surface. Length of a curve on a surface. Angle of two curves. Area of a surface. - Projection of a surface onto a surface, development. Developable surfaces. - The second Fundamentals form of a surface. - Asymptotic curves and principle curves on a surface. - Geodetic curves.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Home preparation for classes
- 6 hours per semester
- Preparation for credit
- 14 hours per semester
- Class attendance
- 42 hours per semester
- Preparation for exam
- 28 hours per semester
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Learning outcomes
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The content of this subject is based on elements of classical differential geometry of curves and spa-ces in three-dimensional Eucliden space: definition of a curve, natural thrihedron, curvatures, osculati-on; definition of a surface, fundamental forms, projection of a surface onto a surface, development, special classes of surfaces. Everything completed with constructive applications.
Elements of classical differential geometry of curves and spa-ces in three-dimensional Eucliden space: definition of a curve, natural thrihedron, curvatures, osculati-on; definition of a surface, fundamental forms, projection of a surface onto a surface, development, special classes of surfaces. Everything completed with constructive applications.
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Prerequisites
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KA1, KA2, FPV
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Assessment methods and criteria
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Oral exam, Written exam
Credit: Active participation on seminars + tests. Exam: writtten.
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Recommended literature
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Boček, L. - Kubát, V.:. Diferenciální geometrie křivek a ploch. Praha, SPN (MFF KU) 1983..
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Budinský, L. - Kepr, B.:. Základy diferenciální geometrie. Praha, SNTL 1970..
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Budinský, L.:. Analytická a diferenciální geometrie. Praha, SPN 1983..
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Pecina, V.:. Základy diferenciální geometrie. [Studijní text TUL], Liberec 2000..
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