| Course Unit Code | 310-3341/01 |
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| Number of ECTS Credits Allocated | 4 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 | 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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| KRC76 | Mgr. Jiří Krček |
| Summary |
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| 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. |
| 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 atc. |
| 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., New York etc., 1993
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Vlček, J.: Vektorová a tenzorová analýza - sylabus k předmětu v LMS.
Míka, S.: Matematická analýza III (Tenzorová analýza). ZČU Plzeň, 1993
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| Recommended Reading: |
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Maxum, B.: Field Mathematics for Electromagnetics, Photonics and Material Science. SPIE Press, Bellingham, USA, 2004
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Brdička, M.: Mechanika kontinua. Academia, Praha 2005
Lenert, J.: Základy matematické teorie pružnosti. VŠB-TU Ostrava, 1997 |
| 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 |