714-0433/02 – Tensor Analysis (TA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelundergraduate or graduateRequirementOptional
Year1Semestersummer
Study languageCzech
Year of introduction2003/2004Year of cancellation2018/2019
Intended for the facultiesFEIIntended for study typesFollow-up Master, Master
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+2
Combined Credit and Examination 2+2

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 elements of tensor algebra and tensor analysis in cartesian and/or orthogonal curvilinear coordinate systems. Tensor fields are studied using local and global characteristics. The applications are illustrated in static and dynamic elasticity as well as on several problems of electromagnetic field in anisotropic materials. More of applications (hydrodynamics et al.) can be chosen when needed.

Compulsory literature:

Akivis, M. A. - Goldberg, V. V.: An Introduction to Linear Algebra and Tensors. Dover Publ., New York etc., 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

Course-credit: -participation on tutorials is obligatory, 20% of absence can be apologized, -pass the written test (point classification: 0-20 points) Exam Semestral thesis classified by 50 points. Theoretical 20 points

E-learning

www.mdg.vsb.cz

Další požadavky na studenta

Individual semestral project

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: material anisotropy in optics, thermoelasticity atc.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester, validity until: 2009/2010 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
        Exercises evaluation Credit 30 (30) 0
                Project Project 30  0
        Examination Examination 70 (70) 0
                Written examination Written examination 70  0
Mandatory attendence parzicipation:

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2018/2019 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2017/2018 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2016/2017 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P English Ostrava 1 Optional study plan
2015/2016 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K English Ostrava 1 Optional study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2014/2015 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2013/2014 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2012/2013 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2011/2012 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2010/2011 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2009/2010 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2008/2009 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2007/2008 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics P Czech Ostrava 1 Optional study plan
2006/2007 (N2647) Information and Communication Technology (1103T031) Computational Mathematics K Czech Ostrava 1 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner