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Lecturer(s)
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Botur Michal, doc. Mgr. Ph.D.
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Broušek Martin, Mgr.
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Peška Patrik, RNDr. Ph.D.
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Course content
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Affine spaces. Definition and properties of affine spaces, points and vectors, affine coordinates. Affine subspaces. Definition, parametric equations, position of affine subspaces. Affine mappings. Definition and properties of mappings and transformations, principal examples of affine mappings and tranformations (translation, rotation, symmetries), matrices of mappings. Euclidean spaces and subspaces, cartesian coordinates, deviation and distance of subspaces, isometric mappings. Differential geometry on curves. Point and vector functions, its limit and derivation, curves and its tangent properties, curves path, Frenet formulas.
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Learning activities and teaching methods
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Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
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Learning outcomes
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Understand basic principles on analytical geometry and differential geometry on curves.
1. Knowledge Describe properties of affine and euclidian spaces and differential geometry on curves.
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Prerequisites
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Knowledge of principles of linear algebra.
KAG/MA1AA and KMA/MA2AA
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Assessment methods and criteria
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Oral exam, Written exam
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Recommended literature
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Bican L. (2004). Lineární algebra a geometrie. Praha, Academia.
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Budinský B. (1983). Analytická a diferenciální geometrie. SNTL Praha.
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Horák P., Janyška J. (2002). Analytická geometrie. Masarykova univerzita.
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JUKL Marek. (2014). Analytická geometrie. Olomouc.
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Kuiper, N.H. (2016). Linear Algebra and Geometry. Haerbin gong ye da xue chu ban she.
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Poole, D. (2014). Linear Algebra: A Modern Introduction. Cengage Learning.
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Pressley A. (2001). Elementary Differential Geometry. Springer.
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Riddle D.R. (1998). Analytic Geometry. Brooks Cole.
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Tapp, K. (2016). Differential Geometry of Curves and Surfaces. Springer.
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Žára J., Felkel P., Beneš B., Sochor J. (2005). Moderní počítačová grafika, 2. vydání. Computer Press.
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