MU05086 Analytic Geometry II

Mathematical Institute in Opava
Summer 2019
Extent and Intensity
2/2/0. 6 credit(s). Type of Completion: zk (examination).
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
Prerequisites (in Czech)
MU05083 Analytic Geometry || MU05084 Analytic Geometry I || MU05085 Analytic Geometry I
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives (in Czech)
Obsahem prednášek je analytický přístup ke studiu lineárnich zobrazení, kuželoseček a kvadrik v projektivní, afinní a eukleidovské rovině a prostoru.
Syllabus
  • Affine maps. Group of affine maps. Fixed points and directions of affine maps. Basic affinities. Module of affinity, equiaffinity. Classification of affinities in the plane. Congruences of Euclidean space. Group of congruences. Reflection in a hyperplane. Symmetries in Euclidean space. Classification of congruences on a line, a plane and in three-dimensional Euclidean space.
    Similarities. Group of similarities. Classification of similarities in the plane. Conic sections. Basic metric theory of conics. Algebraic curves of second order. Central and non-central curves of second order. Diameters of curves of second order. Quadrics. Bilinear and quadratic forms. Classification of quadrics. Quadrics in three-dimensional space. Tangent planes of surfaces of second order.
Literature
    recommended literature
  • J. Janyška, A. Sekaninová. Analytická teorie kuželoseček a kvadrik. Brno, 1996. ISBN 80-210-1435-0. info
  • M. Sekanina. Analytická geometrie II. Praha, 1989. info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is also listed under the following terms Summer 1998, Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2011, Summer 2012, Summer 2013, Summer 2014, Summer 2015, Summer 2016, Summer 2017, Summer 2018.
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