310-3341/01 – Tensor Analysis (TA)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits4
Subject guarantorMgr. Jiří KrčekSubject version guarantorMgr. Jiří Krček
Study levelundergraduate or graduateRequirementChoice-compulsory type B
Year1Semestersummer
Study languageCzech
Year of introduction2019/2020Year of cancellation
Intended for the facultiesFEIIntended for study typesFollow-up Master, Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
KRC76 Mgr. Jiří Krček
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 10+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 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

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

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: 2019/2020 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  10
        Examination Examination 70  21 3
Mandatory attendence participation: The mandatory participation is 80 %. To complete the credit, students must pass the credit tests.

Show history

Conditions for subject completion and attendance at the exercises within ISP: In order to complete the credit, students must pass the credit test. On the basis of a successfully completed credit, they can take an exam, which consists of a semestral project defence and a theoretical part.

Show history

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2024/2025 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Choice-compulsory type B study plan
2024/2025 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Choice-compulsory type B study plan
2023/2024 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Choice-compulsory type B study plan
2023/2024 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Choice-compulsory type B study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Choice-compulsory type B study plan
2022/2023 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Choice-compulsory type B study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Choice-compulsory type B study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Choice-compulsory type B study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Choice-compulsory type B study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Choice-compulsory type B study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 1 Choice-compulsory type B study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 1 Choice-compulsory type B study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction



2023/2024 Summer