The content of the course is the coordinated geometry, mainly the studying of linear objects in affine and Euclidean spaces. The main goal of the course is to explain the theory, which generalizes the knowledge of students on geometry in plane and space from high schools. In the course, we focus on solution intersection and distance problems. Summary: 1. Affine spaces. 2. Affine frames and coordinates. 3. Affine subspaces and their description. 4. Intersection problems for affine subspaces. 5. Sheaves of hyperplanes. 6. Distinguished subsets; half-spaces, angles, convex sets, simplices. 7. Euklidean spaces. 8. Orthonormal frames and coordinates. 9. Perpendicular subspaces, normal line of hyperplane. 10. Cross product, Gramm determinant, volume of parallelepiped. 11. Distance and angle between subspaces. 12. Affine mappings and affine transformations. Content of practicals: Solving of concrete problems demonstrating the theory.
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book), Individual preparation for exam
- Preparation for classes
- 56 hours per semester
- Preparation for exam
- 56 hours per semester
- Class attendance
- 56 hours per semester
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Budínský B., Analytická a diferenciální geometrie, Praha, SNTL, 1983, 296 stran..
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Horák P., Janyška J., Analytická geometrie, Brno, Masarykova univerzita, 1997, 151 stran..
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Leischner P., Geometrická zobrazení, Č. Budějovice, Jihočeská univerzita, 2010, 120. stran..
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Pech P., Afinní bodový prostor, Č. Budějovice, Pedagogická fakulta, Jihočeská univerzita, 1996, 46 stran..
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Pech P., Analytická geometrie lineárních útvarů, Č. Budějovice, Jihočeská univerzita, 2004, 162 stran..
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Pech P., Euklidovský prostor, Č. Budějovice, Pedagogická fakulta, Jihočeská univerzita, 1997, 51 stran..
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Pech P., Strobl J., Analytická geometrie lineárních útvarů, Pedagogická fakulta, Jihočeská univerzita, Č. Budějovice, 1994, 158 stran..
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Sekanina M. a kol., Geometrie I, Praha, SPN, 1986, 197 stran..
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Sekanina M. a kol., Geometrie II, Praha, SPN, 1988, 307 stran..
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