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Lecturer(s)
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Valentová Ivana, doc. Ing. Ph.D.
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Course content
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Week 1: Functions of several variables, their graph, partial derivatives, total differential.. Week 2: Higher order partial derivatives. Week 3: Fundamental notions of min/max theory in Rn; Week 4: Double integral, Fubini theorem. Methods to computation. Week 5: Change of variables in a double integrals Week 6: Triple integral, methods to computation. change of variables. Week 7: Scalar field, gradient, directional derivative. Week 8: Vector fields, divergence and curl. Operator Laplace, Hamilton. Week 9: Paths and parametrizations. Path integrals of scalar fields. Week 10: Path integrals of vector fields, Week 11: Surface integral of scalar fields. Week 12: Surface integral of vector fields. Week 13: Integration theorems of vector calculus
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Learning activities and teaching methods
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Interactive lecture, Task-based study method, Students' self-study
- Contact hours
- 39 hours per semester
- Preparation for formative assessments (2-20)
- 15 hours per semester
- Preparation for comprehensive test (10-40)
- 25 hours per semester
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| prerequisite |
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| Knowledge |
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| No particular prerequisites specified. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: compute partial derivatives of functions of more variables, formulate basic min/max problems of Rn, define and use scalar and vector fields, evaluate double and triple integrals, change of variables in a double and triple integrals, integration along paths and over surfaces. |
| teaching methods |
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| Interactive lecture |
| Task-based study method |
| Self-study of literature |
| assessment methods |
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| Combined exam |
| Test |
| Skills demonstration during practicum |
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Recommended literature
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Drábek, Pavel; Míka, Stanislav. Matematická analýza II.. 4. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7082-977-X.
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Mašek, Josef. Sbírka úloh z matematiky : diferenční rovnice a transformace Z. 1. vyd. Plzeň : ZČU, 1998. ISBN 80-7082-457-3.
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Mašek, Josef. Sbírka úloh z matematiky : integrální transformace. 1. vyd. Plzeň : ZČU, 1993. ISBN 80-7082-117-5.
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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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Polák, Josef. Funkční posloupnosti a řady ; Fourierovy řady. 2. upr. vyd. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-282-9.
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Polák, Josef. Integrální a diskrétní transformace. 3.,přeprac. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-924-9.
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Polák, Josef. Matematická analýza v komplexním oboru II/. 1. vyd. Plzeň : Západočeská univerzita, 2000. ISBN 80-7082-700-9.
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Polák, Josef. Matematická analýza v komplexním oboru. 2., upr. vyd. Plzeň : Západočeská univerzita, 2002. ISBN 80-7082-923-0.
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