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Lecturer(s)
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Jukl Marek, doc. RNDr. Ph.D.
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Juklová Lenka, RNDr. Ph.D.
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Course content
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1. Affine spaces, affine coordinates, affine subspaces, expression of subspaces by means of equations, relative position of affine subspaces. 2. Barycentric coordinates. 3. Oriented affine lines, ordered affine lines, half-lines, abscissas. 4. Oriented affine spaces, half-spaces. 5. Affinity. 6. Euclidean spaces, metric, distance of subspaces. 7. Angle of subspaces. 8. Volume of a simplex. 9. Isometry. 10. Quadratic and bilinear forms, polar bases, signatures. 11. Diagonalisation of the matrix of a real quadratic form. 12. Conics in the Euclidean plane. Canonical equations. 13. Line and conic. 14. Metric and affine classification of conics, affine and metric invariants. 15. Quadratic surfaces in a 3-dimmensional Euclidean space (quadrics). Canonical equations. 16. Lines and quadrics. Planes and quadrics. 17. Affine classification of quadrics. 18. Plane and quadric.
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Learning activities and teaching methods
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Monologic Lecture(Interpretation, Training), Dialogic Lecture (Discussion, Dialog, Brainstorming), Demonstration
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Learning outcomes
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Understand analytic geometry of linear subsets of affine and Euclidean spaces of general dimension. To master corresponding tasks. Understand the analytic geometry of conics and quadrics in Euclidean plane resp. 3-dimensional space. To master corresponding tasks.
1. Knowledge Students recall basic knowledges of linear algebra and describe elements of coordinated linear affine and Euclidean geometry and define relations between geometrical configurations. Students describe elements of coordinated geometry of quadrics in euclidean plane and 3-dimensional space and define relations between quadrics and other geometrical configurations.
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Prerequisites
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unspecified
KAG/KALI
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Assessment methods and criteria
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Written exam, Student performance
The student has to participate actively in seminars and pass a written test.
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Recommended literature
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Sekanina M. (1986). Geometrie I. SPN Praha.
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Berger, M. (2004). Geometry I, II. Universitext Springer-Verlag Berlin.
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Hejný M. (1985). Geometria I. SPN Bratislava.
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JUKL Marek. Analytická geometrie. Olomouc.
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Marková L. (1991). Cvičení z geometrie I. VUP Olomouc.
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Zlatoš P. (2011). Lineárna algebra a geometria. Bratislava.
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