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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: Laplace transform, inverse transform, solving linear constant coefficient differential equations using Laplace transform Week 2: Double integral, Fubini theorem. Methods to computation. Change of variables in a double integrals. Week 3: Triple integral. Methods to computation. Week 4: Scalar field, gradient, directional derivative. Week 5: Vector fields, divergence and curl. Operator Laplace, Hamilton. Week 6: Paths and parametrizations. Path integrals of scalar fields. Path integrals of vector fields, Week 7: Parametrized surfaces. Surface integral of scalar and vector fields. Integration theorems of vector calculus. Week 8: Series of real number, conergent and divergent series. Week 9: Sequences of functions, point-wise and uniform konvergence. Week 10-11: Power series and their convergence. Taylor's series Week 12-13: Fourier series.
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Learning activities and teaching methods
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Interactive lecture, Task-based study method, Students' self-study
- Preparation for formative assessments (2-20)
- 24 hours per semester
- Contact hours
- 78 hours per semester
- Preparation for an examination (30-60)
- 56 hours per semester
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| prerequisite |
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| Knowledge |
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| Students should be familiar with basic notions of the course KMA/ZME1, KMA/ZME2. |
| learning outcomes |
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| By the end of the course, a successful student should be able to: Evaluate double and triple integral, parametrization of curves and surfaces, evaluate line and surfece integral. Deal with function sequences and function series. Expend a function into Fourier series. |
| 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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Jirásek, František; Kriegelstein, Eduard; Tichý, Zdeněk. Sbírka řešených příkladů z matematiky : logika a množiny, lineární a vektorová algebra, analytická geometrie, posloupnosti a řady, diferenciální a integrální počet funkcí jedné proměnné. 2. nezměn. vyd. Praha : SNTL, 1981.
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Jirásek, František; Vacek, Ivan; Čipera, Stanislav. Sbírka řešených příkladů z matematiky II. 1. vyd. Praha : SNTL, 1989.
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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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Polák, Josef. Funkční posloupnosti a řady, Fourierovy řady. 1. vyd. Plzeň : Západočeská univerzita, 1995. ISBN 80-7082-224-4.
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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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