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Lecturer(s)
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Tobiáš Jiří, PhD
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Caletka Tomáš, RNDr. CSc.
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Course content
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Vector differential calculus. Curves and Surfaces. Line and surface integrals. Gradient of a scalar field, divergence and curl of a vector field. Transformation of coordinate systems. Vector and tensor fields. Transformation rules for tensors. Divergence theorem of Gauss. Stokes theorem. Greens theorems. Formulation of physical laws.
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Learning activities and teaching methods
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Multimedia supported teaching, Lecture, Practicum
- Contact hours
- 65 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Preparation for comprehensive test (10-40)
- 30 hours per semester
- Preparation for an examination (30-60)
- 51 hours per semester
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| prerequisite |
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| Knowledge |
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| There is no prerequisite for this course. Students should be familiar with basic notions of mathematical analysis to the extent of the course KMA/MA1, KMA/MA2. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: 1. Define a simple regular curve, its tangent and natural parametrization; 2. Define curve's integral of the first and second type; 3. Formulate Green's theorem; 4. Define gradient of a scalar field, divergence and curl of a vector field; 5. Define a smooth and closed surface; 6. Define and describe surface's integral of the first and second type; 7. Formulate Gauss theorem; 8. Formulate Stokes theorem; 9. Use curvilinear coordinates, contravariant a covariant vectors; 10. Define tensors of rank zero, one and two. |
| teaching methods |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| assessment methods |
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| Combined exam |
| 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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Zachariáš, Svatopluk. Úvod do vektorové a tenzorové analýzy. 1. vyd. Plzeň : ZČU, 1998. ISBN 80-7082-445-X.
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