# 714-0433/02 – Tensor Analysis (TA)

 Gurantor department Department of Mathematics and Descriptive Geometry Credits 4 Subject guarantor doc. RNDr. Jaroslav Vlček, CSc. Subject version guarantor doc. RNDr. Jaroslav Vlček, CSc. Study level undergraduate or graduate Requirement Optional Year 1 Semester summer Study language Czech Year of introduction 2003/2004 Year of cancellation 2018/2019 Intended for the faculties FEI Intended for study types Master, Follow-up Master
Instruction secured by
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
Part-time 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

www.mdg.vsb.cz

### Other requirements

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: 2011/2012 Winter semester)
Min. number of points
Exercises evaluation and Examination Credit and Examination 100 (100) 51
Exercises evaluation Credit 30 (30) 0
písemný test Written test 30  0
Examination Examination 70 (70) 0
semestrální projekt Semestral project 50  21
teorie Oral examination 20  0
Mandatory attendence parzicipation:

Show history

### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy 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