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Lecturer(s)
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Course content
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Week 1: Domain of functions of two variables, their graph. Level curves of the function Week 2: Partial derivatives, chain rule, implicite functions, Week 3: Fundamental notions of min/max theory in R2. Week 4: Double integral. 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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Seminar classes, Seminar, Practicum
- Contact hours
- 26 hours per semester
- Preparation for formative assessments (2-20)
- 10 hours per semester
- Preparation for comprehensive test (10-40)
- 18 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/ME1. |
| 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, evaluate double and triple integrals, change of variables in a double integrals, integration along paths and over surfaces. |
| teaching methods |
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| Seminar |
| Practicum |
| Seminar classes |
| assessment methods |
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| Test |
| Skills demonstration during practicum |
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Recommended literature
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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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Polák, Josef. Funkční posloupnosti a řady ; Fourierovy řady. 2. upr. vyd. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-282-9.
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