Course: Mathematics 3

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Course title Mathematics 3
Course code KAG/MA3AA
Organizational form of instruction Lecture + Exercise
Level of course Bachelor
Year of study not specified
Semester Summer
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Dušek Zdeněk, doc. RNDr. Ph.D.
  • Mikeš Josef, prof. RNDr. DrSc.
  • Botur Michal, doc. Mgr. Ph.D.
  • Broušek Martin, Mgr.
Course content
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.

Learning activities and teaching methods
Lecture, Dialogic Lecture (Discussion, Dialog, Brainstorming)
Learning outcomes
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.
Prerequisites
Knowledge of principles of linear algebra.
KAG/MA1AA and KMA/MA2AA

Assessment methods and criteria
Oral exam, Written exam

Recommended literature
  • Bican L. (2004). Lineární algebra a geometrie. Praha, Academia.
  • Budinský B. (1983). Analytická a diferenciální geometrie. SNTL Praha.
  • Horák P., Janyška J. (2002). Analytická geometrie. Masarykova univerzita.
  • Pressley A. (2001). Elementary Differential Geometry. Springer.
  • Riddle D.R. (1998). Analytic Geometry. Brooks Cole.
  • Žára J., Felkel P., Beneš B., Sochor J. (2005). Moderní počítačová grafika, 2. vydání. Computer Press.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Computer Science (1) Informatics courses 2 Summer