310-3341/02 – Tensor Analysis (TA)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 4 |
| Subject guarantor | Mgr. Jiří Krček | Subject version guarantor | Mgr. Jiří Krček |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory type B |
| Year | 1 | Semester | summer |
| | Study language | English |
| Year of introduction | 2019/2020 | Year of cancellation | |
| Intended for the faculties | FEI | Intended for study types | Master, Follow-up Master |
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
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
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