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Vector and tensor analysis

* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code310-3242/01
Number of ECTS Credits Allocated3 ECTS credits
Type of Course Unit *Choice-compulsory type B
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
KUC14prof. RNDr. Radek Kučera, Ph.D.
KRC76Mgr. Jiří Krček
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.
Learning Outcomes of the Course Unit
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.
Course Contents
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.
Recommended or Required Reading
Required Reading:
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
Vlček, J.: Vektorová a tenzorová analýza - sylabus k předmětu v LMS.
Brdička, M.: Mechanika kontinua. Academia, Praha 2005
Hess, S.: Tensors for Physics, Springer, 2015
Recommended Reading:
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
Míka, S.: Matematická analýza III (Tenzorová analýza). ZČU Plzeň, 1993
Lenert, J.: Základy matematické teorie pružnosti
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit30 10
        ExaminationExamination70 21