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

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits10
Subject guarantorprof. RNDr. Radek Kučera, Ph.D.Subject version guarantorprof. RNDr. Radek Kučera, Ph.D.
Study levelpostgraduateRequirementChoice-compulsory
YearSemesterwinter + summer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFMT, FSIntended for study typesDoctoral
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
KUC14 prof. RNDr. Radek Kučera, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Examination 28+0
Part-time Examination 28+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/

Other requirements

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

Part-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)		Min. number of pointsMax. počet pokusů
Examination Examination   3
Mandatory attendence participation:

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Conditions for subject completion and attendance at the exercises within ISP:

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