Course Unit Code | 310-3242/01 |
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Number of ECTS Credits Allocated | 3 ECTS credits |
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Type of Course Unit * | Choice-compulsory type B |
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Level of Course Unit * | Second Cycle |
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Year of Study * | First Year |
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Semester when the Course Unit is delivered | Winter Semester |
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Mode of Delivery | Face-to-face |
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Language of Instruction | Czech |
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Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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Name of Lecturer(s) | Personal ID | Name |
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| KUC14 | prof. RNDr. Radek Kučera, Ph.D. |
| KRC76 | Mgr. Jiří Krček |
Summary |
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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.
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Learning Outcomes of the Course Unit |
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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.
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Course Contents |
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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.
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Recommended or Required Reading |
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Required Reading: |
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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: |
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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
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Planned learning activities and teaching methods |
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Lectures, Individual consultations, Tutorials, Project work |
Assesment methods and criteria |
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Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing |
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Credit and Examination | Credit and Examination | 100 (100) | 51 |
Credit | Credit | 30 | 10 |
Examination | Examination | 70 | 21 |