714-0921/02 – Differential Geometry (DifG)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantordoc. RNDr. Pavel Burda, CSc.Subject version guarantordoc. RNDr. Pavel Burda, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2007/2008Year of cancellation2010/2011
Intended for the facultiesFEI, USP, FBI, FAST, FS, HGF, FMTIntended 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

Developing of programs according to assign.

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Curves in the plane and in space. 2. Curvature. 3. Global properties of curves. 4. Surfaces in three dimension. 5. Tangents, normals. 6. Examples of surfaces. 7. Quadratic surfaces. 8. Lenghts of curves on surfaces. 9. Isometries on surfaces, conformal mappings. 10. Surface area. 11. The curvature of curves on surface. 12. Normal and principal curvatures. 13. Geometrical interpretacion.

Conditions for subject completion

Combined form (validity from: 2009/2010 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:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2009/2010 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2009/2010 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2008/2009 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V007) Hydraulics and Pneumatics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2007/2008 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner