310-4000/01 – Vector and Tensor Analysis (VeTeA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEI, FBI, FAST, FMT, HGF, USP, FSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KUC14 prof. RNDr. Radek Kučera, Ph.D.
VLC20 doc. RNDr. Jaroslav Vlček, CSc.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+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 Publications, 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

Continuous work on project assignment.

E-learning

http://mdg.vsb.cz/portal/

Další požadavky na studenta

No additional requirements are prescribed.

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Orthogonal transformation, Cartesian tensors, tensor algebra 2. Vector and tensor field, derivatives and differential operators 3. Curvilinear and surface integrals, integral theorems 4. Local and global characteristics of vector fields 5. Fundamentals of tensor apparatus in static theory of elasticity 6. Equations of dynamic theory of elasticity 7. Facultative themes: anisotropy of materials, thermoelasticity etc.

Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Examination Examination  
Mandatory attendence parzicipation:

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Occurrence in study plans

Academic yearProgrammeField of studySpec.FormStudy language Tut. centreYearWSType of duty
2019/2020 (P3924) Materials Science and Engineering P Czech Ostrava Choice-compulsory study plan
2019/2020 (P3924) Materials Science and Engineering K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling P Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2301V013) Robotics P Czech Ostrava Choice-compulsory study plan
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2019/2020 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment P Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology P Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3901V003) Applied Mechanics P Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes P Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2301V001) Transport and Material Handling K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2301V013) Robotics K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2302V006) Energy Engineering K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2302V019) Contruction of Production Machines and Equipment K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (2303V002) Mechanical Engineering Technology K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3901V003) Applied Mechanics K Czech Ostrava Choice-compulsory study plan
2019/2020 (P2346) Mechanical Engineering (3902V056) Control of Machines and Processes K Czech Ostrava Choice-compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner