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Lecturer(s)
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Pertlíček Jan, PhD
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Bosman Luboš, RNDr.
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Fillová Gabriela, doc. Ing. Ph.D.
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Course content
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1. Bases and coordinates, Einstein summation convention 2. Transformation of bases 3. Curvilinear coordinates 4. Tensor propedeutics 5. Tensor algebra 6. Tensor analysis 7. Vector fields 8. Field in a curvilinear system 9. Varieties and their description 10. Curvilinear integrals 11. Surface integrals 12. Integral characteristics of fields 13. Reserve
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Learning activities and teaching methods
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Multimedia supported teaching, Lecture, Practicum
- Preparation for comprehensive test (10-40)
- 20 hours per semester
- Contact hours
- 65 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Preparation for an examination (30-60)
- 35 hours per semester
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| prerequisite |
|---|
| Knowledge |
|---|
| understand the basic principles of linear algebra |
| understand the basic principles of differential calculus of functions of one and more variables |
| understand the basic principles of integral calculus of functions of one and more variables |
| Skills |
|---|
| parametrize basic curves |
| perform arithmetic operations with vectors and matrices |
| differentiate functions of one and more variables |
| calculate single, double and triple integrals |
| Competences |
|---|
| N/A |
| N/A |
| N/A |
| N/A |
| learning outcomes |
|---|
| Knowledge |
|---|
| understand the description of quantities in different coordinate systems |
| understand the basic concepts and principles of tensor calculus |
| understand the differential characteristics of tensor fields |
| understand the integral characteristics of tensor fields |
| Skills |
|---|
| calculate the covariant and contravariant coordinates of the vector |
| determine differential characteristics of vector fields |
| calculate curve and surface integrals |
| apply Green, Stokes and Gauss Theorems |
| Competences |
|---|
| N/A |
| N/A |
| N/A |
| teaching methods |
|---|
| Knowledge |
|---|
| Task-based study method |
| Interactive lecture |
| Practicum |
| Skills |
|---|
| Practicum |
| Task-based study method |
| Interactive lecture |
| Competences |
|---|
| Task-based study method |
| Interactive lecture |
| Practicum |
| assessment methods |
|---|
| Knowledge |
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| Continuous assessment |
| Test |
| Combined exam |
| Skills |
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| Combined exam |
| Test |
| Continuous assessment |
| Competences |
|---|
| Combined exam |
| Continuous assessment |
| Test |
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Recommended literature
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Boček, Leo. Tenzorový počet. 1. vyd. Praha : SNTL, 1976.
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Míka, Stanislav. Matematická analýza III : tenzorová analýza. 1. vyd. Plzeň : Západočeská univerzita, 1993. ISBN 80-7082-115-9.
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Spiegel Murray R. Schaum's Outline of Theory and Problems of Vector Analysis and An Introduction to Tensor Analysis. McGraw-Hill Book Company, Singapure, 1959. ISBN 0-07-084378-3.
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Zachariáš, Svatopluk. Úvod do vektorové a tenzorové analýzy. 1. vyd. Plzeň : ZČU, 1998. ISBN 80-7082-445-X.
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