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Course Catalogue MU:MU01907 Geometry - Exercises - Course Information Tato aplikace je zatím určena pro spuštění na stolním počítači. Na tomto mobilním zařízení je také funkční, ale zatím plně nevyužívá jeho možností.

Tato aplikace je zatím určena pro spuštění na stolním počítači. Na tomto mobilním zařízení je také funkční, ale zatím plně nevyužívá jeho možností.

MU:MU01907 Geometry - Exercises - Course Information

MU01907 Geometry - Exercises

Mathematical Institute in Opava
Summer 2011

Extent and Intensity

0/1/0. 1 credit(s). Type of Completion: z (credit).

Teacher(s)

RNDr. Adam Hlaváč, Ph.D. (seminar tutor)

Guaranteed by

doc. RNDr. Michal Marvan, CSc.
Mathematical Institute in Opava

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

Applied Mathematics (programme MU, B1101)
Applied Mathematics in Risk Management (programme MU, B1102)
Geometry (programme MU, M1101)
Mathematical Analysis (programme MU, M1101)
Mathematical Methods in Economics (programme MU, B1101)
Mathematics (programme MU, B1101)
Theoretical Physics (programme FPF, M1701 Fyz)
Theoretical Physics (programme FPF, N1701 Fyz)
Secondary School Teacher Traning in Physics and Mathematics (programme FPF, M1701 Fyz)
Secondary School Teacher Training in Mathematics (programme FPF, M7504)
Secondary school teacher training in general subjects with specialization in Mathematics (programme FPF, M7504)

Course objectives

Exercises to Geometry.

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

Written examination.

The course is also listed under the following terms Summer 2000, Summer 2001, Summer 2002, Summer 2003, Summer 2004, Summer 2005, Summer 2006, Summer 2007, Summer 2008, Summer 2009, Summer 2010, Summer 2012, Summer 2013, Summer 2014, Winter 2014, Winter 2015, Winter 2016, Winter 2017, Winter 2018, Winter 2019, Winter 2020, Winter 2021.

Enrolment Statistics (Summer 2011, recent)
Permalink: https://is.slu.cz/course/sumu/summer2011/MU01907

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