MU05085 Analytic Geometry I

Mathematical Institute in Opava
Winter 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: z (credit).
Teacher(s)
RNDr. Petr Vojčák, Ph.D. (lecturer)
RNDr. Petr Vojčák, Ph.D. (seminar tutor)
Guaranteed by
RNDr. Petr Vojčák, Ph.D.
Mathematical Institute in Opava
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives (in Czech)
Předmět slouží k seznámení se základy analytické geometrie. Obsahem seminářů je řešení příkladů k jednotlivým tématům látky probírané na přednáškách.
Syllabus
  • Affine spaces. Linear subspaces, their parametric expression and expression in equations. Mutual positions of subspaces. Intersection and span of subspaces. Line orderings. Parallelism. Transversal of skew lines. Orientation. Half-lines, half-spaces. Coordinate transformations in affine space. Linear forms.
    Metric spaces, examples. Euclidean space. Center of a pair of points. Inner product. Orthogonality of vectors, directions and subspaces. Orthogonal complement. Pseudo-inner product. Distance of subspaces. Axis of skew lines. Linear forms in Euclidean space. Coordinate transformations in Euclidean space. Definition of the angle. Angles of half-lines, lines, a line and a subspace. Projective extension of Euclidean space. Homogeneous coordinates. Double ratio.
Literature
    recommended literature
  • P. Horák, J. Janyška. Analytická geometrie. Brno, 1997. info
  • M. Sekanina a kol. Analytická geometrie I. Praha, 1986. info
Language of instruction
Czech
Further comments (probably available only in Czech)
Study Materials
The course can also be completed outside the examination period.
The course is also listed under the following terms Winter 1997, Winter 1999, Winter 2000, Winter 2001, Winter 2002, Winter 2003, Winter 2004, Winter 2005, Winter 2006, Winter 2007, Winter 2008, Winter 2009, Winter 2010, Winter 2011, Winter 2012, Winter 2013, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018.
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