Předmět Geometry 2 (KMA / WENE2)
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Další informace
Obsah
Programme of the Course1.Topological space.2.Vector functions.3.Curves in Euclidean space, smooth curve, the arc of the curve, the natural parameterization.4.Frenet trihedron, Frenet formulas, flexion and torsion.5.Application of Frenet formulas.6.Planar curves.7.Surfaces in Euclidean space, tangent and normal to the surface, the coordinate curves.8.The 1st quadratic differential form of a surface and its application.9.The 2nd quadratic form of a surface and its application ? normal curvature, Dupin indicatrix.10.Asymptotic curves of the surface, the principal curvature and principal curves of the surface.11.The median and Gaussian curvature of a surface, Egregium theorem, classification of points on the surface.12.Geodesic curvature and geodesic curves of the surface, Gauss-Bonnet theorem and its specialization for geodesic triangles of the surface.
Literatura
RIDDLE, D. R. Analytic geometry. Brooks Cole, 1998. DO CARMO M. P. Differential Geometry of Curves and Surfaces. LIPSCHULTZ, M. M. Differential Geometry. Schaums Outline Series in Mathematics. Pressley, A. Elementary diffrential geometry, Springer 2001. THORPE, J. A. Elementary Topics in Differencial Geometry. Springer-Verlag, 1979.
Požadavky
Students have to pass two written examinations during the semester. Students can earn a maximum 100 points. The evaluation of the course including the classification is carried out in accordance with the Study and Examination Regulations OU.
Garant
RNDr. Radka Malíková, Ph.D.
Vyučující
RNDr. Radka Malíková, Ph.D.RNDr. Radka Malíková, Ph.D.