714-0921/01 – Differential Geometry (DifG)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits0
Subject guarantordoc. RNDr. Pavel Burda, CSc.Subject version guarantordoc. RNDr. Pavel Burda, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction1997/1998Year of cancellation2009/2010
Intended for the facultiesIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
BUR30 doc. RNDr. Pavel Burda, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+0
Combined Credit and Examination 0+0

Subject aims expressed by acquired skills and competences

Main study goals: (i) to be acquainted with actual progress in this mathematical discipline, (ii) to extend needed theoretical knowledge with emphasized orientation to its applica-bility, (iii) to increase communication ability of specialists in different branches. With regard to professional orientation of students learning themes modification is offered to fulfill presented aims.

Teaching methods

Lectures
Individual consultations

Summary

The content of the subject is classic differential geometry of curves and surfaces in spaces E2 and E3. This theory has many applications in classic and relativist mechanics, in cinematic geometry etc.

Compulsory literature:

Pressley, A.: Elementary Differential Geometry, Springer Verlag, London, 2001, ISBN 1-85233-152-6

Recommended literature:

Holme, A.: Geometry. Springer – Verlag, Berlin, Heidelberg, New York, 2002, ISBN 3-540-41949-7. Jennings, G.A.: Modern Geometry with Applications, Springer-Verlag, New York, 1994, ISBN 0-387-94222-X.

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Vektorová funkce skalárního argumentu, geometrický a fyzikální význam, limita, spojitost a derivace vektorové funkce. 2.Některé vlastnosti rovinných křivek, tečna, normála, subtangenta, subnormála, singulární body křivek. 3. Prostorová křivka a Frenetův trojhran, tečna, normálová a oskulační rovina, binormála, rektifikační rovina a hlavní normála. 4. Dvojí křivost prostorové křivky, flexe a torze v bodě, poloměr křivosti rovinné křivky, evoluta a evolventa rovinné křivky. 5. Pojem plochy třídy Ck, tečná rovina a normála plochy. 6. Obálka a hrana vratu soustavy ploch, rozvinutelné a přímkové plochy. 7. První a druhá základní diferenciální forma plochy, diferenciál křivky na ploše, odchylka dvou křivek na ploše. 8. Křivost plochy, klasifikace regulárních bodů plochy. 9. Význačné křivky na ploše, asymptotické a geodetické křivky.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2012/2013 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
        Examination Examination 100  51
        Exercises evaluation Credit 0  0
Mandatory attendence parzicipation:

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