714-0924/05 – Vector and Tensor Analysis (VeTeA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Web linkhttp://mdg.vsb.czStudy languageCzech
Year of introduction2013/2014Year of cancellation
Intended for the facultiesHGF, FEI, FBI, FAST, FMMI, FS, USPIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 0+0
Combined Examination 14+0

Subject aims expressed by acquired skills and competences

Students learn to use tensor calculus. They shlould know how to analyze a problem, to choose and correctly use appropriate algorithm, to apply their knowledge to solve technical problems.

Teaching methods

Lectures
Individual consultations
Tutorials
Project work

Summary

The main goal consist in the elements of tensor algebra and tensor analysis in cartesian and/or orthogonal curvilinear coordinate systems. The properties of tensor fields are studied using local and global characteristics. Applications are illustrated above all in the frame of static and dynamic elasticity as well as on several problems of the electromagnetic fields in anisotropic media.

Compulsory literature:

Akivis, M. A. - Goldberg, V.V.: An Introduction to Linear Algebra and Tensors. Dover Publ., N.Y. 1993

Recommended literature:

Maxum, B.: Field Mathematics for Electromagnetics, Photonics and Material Science. SPIE Press, Bellingham, USA, 2004

Way of continuous check of knowledge in the course of semester

E-learning

www.mdg.vsb.cz

Další požadavky na studenta

No more requirements are put on the student.

Minimální znalostní požadavky

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Orthogonal transformation, Cartesian tensors 2. Tensor algebra 3. Vector and tensor field, derivatives and differential operators 4. Local and global characteristics of vector fields 5. Fundamentals of tensor apparatus in static theory of elasticity 6. Stress and strain tensor, Hooke's law 7. Equations of dynamic theory of elasticity 8. Facultative themes: anisotropy of materials in optics, thermoelasticity atc.

Conditions for subject completion

Prezenční form (validity from: 2013/2014 zimní semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Zkouška Zkouška  
Rozsah povinné účasti:

Zobrazit historii

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2017/2018 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2017/2018 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2017/2018 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2017/2018 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2017/2018 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2017/2018 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2016/2017 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2016/2017 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2016/2017 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2015/2016 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2015/2016 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2015/2016 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2014/2015 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2014/2015 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2014/2015 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2014/2015 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2014/2015 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2013/2014 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V003) Transport Equipment and Technology K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (3902V010) Automation of Technological Processes K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2301) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2013/2014 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2013/2014 (P1701) Physics (1702V001) Applied Physics P Czech Ostrava Choice-compulsory study plan
2013/2014 (P1701) Physics (1702V001) Applied Physics K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner