310-3242/01 – Vector and tensor analysis (VeTeA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits3
Subject guarantordoc. RNDr. Jaroslav Vlček, CSc.Subject version guarantordoc. RNDr. Jaroslav Vlček, CSc.
Study levelundergraduate or graduateRequirementChoice-compulsory
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesUSP, HGF, FMTIntended for study typesFollow-up Master
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 Credit and Examination 2+1

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

Individual consultations
Project work


The main goal consist in the elements of tensor algebra and tensor analysis in cartesian 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 MEJLBRO, L. Calculus 2b – Real Functions in Several Variables. http://bookboon.com/cs/calculus-2b-3-ebook. ISBN 87-7681-206-5 Hess, S.: Tensors for Physics, Springer, 2015

Recommended literature:

Maxum, B.: Field Mathematics for Electromagnetics, Photonics and Materials Science. SPIE Press, Bellingham (USA), 2005 SPIEGEL, R. M., LIPSCHUTZ, S., SPELLMAN, D. Vector Analysis, 2nd edition, McGraw-Hill, 2009, ISBN 978-7161-545-7

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 (30 points), Point classification: 0-30 points. Exam Semestral thesis classified by 25 – 50 points. Theoretical part of the exam is classified by 0 - 20 points.



Other requirements

Participation on tutorials is obligatory, 20% of absence can be apologized Elaboration of semestral project


Subject has no prerequisities.


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, 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
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21
Mandatory attendence parzicipation: 80 %

Show history

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2020/2021 (N0719A270002) Nanotechnology P Czech Ostrava 1 Choice-compulsory type B study plan
2019/2020 (N3942) Nanotechnology (3942T001) Nanotechnology P Czech Ostrava 1 Choice-compulsory study plan
2019/2020 (N0719A270002) Nanotechnology P Czech Ostrava 1 Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner