| Course Unit Code | 310-4000/01 |
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| Number of ECTS Credits Allocated | 10 ECTS credits |
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| Type of Course Unit * | Choice-compulsory |
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| Level of Course Unit * | Third Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Winter, Summer 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 | Course succeeds to compulsory courses of previous semester |
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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 and/or orthogonal curvilinear 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 |
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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, tensor algebra
2. Vector and tensor field, derivatives and differential operators
3. Curvilinear and surface integrals, integral theorems
4. Local and global characteristics of vector fields
5. Fundamentals of tensor apparatus in static theory of elasticity
6. Equations of dynamic theory of elasticity
7. Facultative themes: anisotropy of materials, thermoelasticity etc. |
| 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 Publications, N.Y. 1993 |
Vektorová a tenzorová analýza - sylabus k předmětu. http://homen.vsb.cz/~vlc20/
Brdička, M.: Mechanika kontinua. Academia, Praha 2005
Bowen, R. M., Wang, C.C.: Introduction to vectors and tensors. Dover Publications, N. Y. 2009. ISBN 048646914X |
| Recommended Reading: |
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| Maxum, B.: Field Mathematics for Electromagnetics, Photonics and Material Science. SPIE Press, Bellingham, USA, 2004 |
| Míka, S.: Matematická analýza III (Tenzorová analýza). ZČU Plzeň, 1993 |
| 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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| Examination | Examination | | |