714-0767/01 – Vector and tensor analysis (VeTeA)
| Gurantor department | Department of Mathematics and Descriptive Geometry | Credits | 3 |
| Subject guarantor | doc. RNDr. Jaroslav Vlček, CSc. | Subject version guarantor | doc. RNDr. Jaroslav Vlček, CSc. |
| Study level | undergraduate or graduate | Requirement | Choice-compulsory |
| Year | | Semester | winter |
| | Study language | Czech |
| Year of introduction | 2010/2011 | Year of cancellation | 2019/2020 |
| Intended for the faculties | FMT, HGF, USP | Intended for study types | 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 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:
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
Additional study materials
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.
E-learning
www.mdg.vsb.cz
Other requirements
Participation on tutorials is obligatory, 20% of absence can be apologized
Elaboration of 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, etc.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction