MU01007 Geometry

Mathematical Institute in Opava
Winter 2017
Extent and Intensity
2/0/0. 3 credit(s). Type of Completion: zk (examination).
Teacher(s)
doc. RNDr. Hynek Baran, Ph.D. (lecturer)
Guaranteed by
doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava
Prerequisites (in Czech)
MU01006 Algebra II && ( MU01907 Geometry - Exercises || MU01917 Geometry - Exercises ) && MU01002 Mathematical Analysis II
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
Covering part of the requirements of the Comprehensive Exam in Mathematics, the course introduces basic concepts, methods, and applications of geometry of subspaces, curves and subvarieties in Euclidean space.
Syllabus
  • Affine and Euclidean spaces and subspaces, affine maps and isometries, affine and Cartesian coordinates.
    Distance and inclination of subspaces in Euclidean space, the volume of a parallelepiped.
    Applications in planimetry, stereometry, and coding theory.
    Curves in Euclidean space, parameterization; Frenet frame, curvatures, Frenet--Serret equations; evolutes and involutes.
    Subvartieties in Euclidean space, regular parameterization, tangent space, directional derivative, the first fundamental form, vector field, Lie bracket.
    Hypersurfaces in Euclidean space, normal vector, covariant derivative, the second fundamental form, Gauss--Weingarten equations; parallel displacement, geodesics; principal curvatures.
    Applications in cartography and physics.
Literature
    recommended literature
  • I. Kolář, L. Pospíšilová. Diferenciální geometrie křivek a ploch. URL info
  • M. Marvan. Geometrie lineárních útvarů. 2010. URL info
  • M. Marvan. Geometrie nelineárních útvarů. 2010. URL info
Language of instruction
Czech
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
Teacher's information
A written examination followed by an oral examination.
The course is also listed under the following terms Summer 1998, Summer 1999, 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, Winter 2014, Winter 2015, Winter 2016.
  • Enrolment Statistics (recent)
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