714-0924/01 – 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
Study languageCzech
Year of introduction1997/1998Year of cancellation2012/2013
Intended for the facultiesFBI, FAST, FEI, FS, HGF, USP, FMTIntended 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 Credit and Examination 2+0
Combined Credit and Examination 0+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.

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

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 (145) 51
        Examination Examination 100  0
        Exercises evaluation Credit 45  0
Mandatory attendence parzicipation:

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2002/2003 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2002/2003 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2302V002) Parts of Machines and Mechanisms P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2302V006) Energy Engineering P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2301) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava 1 Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V015) Electronics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2612V045) Technical Cybernetics P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (2642V004) Electrical Machines, Apparatus and Drives P Czech Ostrava Choice-compulsory study plan
2001/2002 (P2612) Electrical Engineering and Computer Science (3907V001) Electrical power Engineering P Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner