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Lecturer(s)
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Zouvalová Katarína, Ing. Ph.D.
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Course content
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Week 1: Functions of several variables, fundamental notions , partial derivatives, total differential, gradient, directional derivative, higher order partial derivatives. Week 2: Fundamental notions of min/max theory in Rn; Week 3: Double integral, Fubini's theorem. Week 4: Change of variables in a double integrals, polar coordinates. Week 5: Triple integral, methods to computation. change of variables. Week 6: Vector fields, divergence and curl. Hamilton operator, potential. Week 7: Laplace operator, Laplace equation, harmonic function. Revision of curves. Week 8: Path integrals of scalar fields. Week 9: Path integrals of vector fields, Week 10: Surfaces and parametrization 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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Lecture, Practicum
- Contact hours
- 52 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
- Preparation for an examination (30-60)
- 32 hours per semester
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| prerequisite |
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| Knowledge |
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| No particular prerequisites specified. |
| Describe derivative and integral of the function of one real variable. |
| Describe basic curves. |
| Explain the geometric meaning of the derivative and integral of the function of one real variable. |
| Skills |
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| To differentiate and integrate the functions of one real variable. |
| To draw basic curves and surfaces. |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| Formulate basic min/max problems of R2 ans R3. |
| Define and use scalar and vector fields of one and several variables. Describe partial derivative, gradient, divergence, circulation and Laplace equation and explain their meaning. |
| Parametric representation of basic surfaces. |
| Describe of double and triple integrals and change of variables. Describe curve and surface integral of scalar and vector fields. Explain their meaning. |
| Formulate Green's theorem, Gauss's theorem, Stokes' theorem. |
| Skills |
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| Find local extrema of the functions of several variables. |
| Evaluate partial derivatives and gradient of scalar field. Evaluate divergence and circulation of vector field. |
| Evaluate simple double and triple integrals, change of variables in a double and triple integrals, integration along paths and over surfaces and use integral theorems. |
| Competences |
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| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Practicum |
| Multimedia supported teaching |
| Skills |
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| Lecture supplemented with a discussion |
| Interactive lecture |
| Practicum |
| One-to-One tutorial |
| Competences |
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| Lecture |
| Practicum |
| Task-based study method |
| assessment methods |
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| Knowledge |
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| Combined exam |
| Test |
| Skills |
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| Combined exam |
| Test |
| Competences |
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| Oral exam |
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Recommended literature
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J. Bouchala, O. Vlach. Křivkový a plošný integrál. 2012.
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J. Kuben, Š. Mayerová, P. Račková, P. Šarmanová. Diferenciální počet funkcí více proměnných. 2012.
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J. Neustupa, S Kračmar. Mathematics II. 1998. ISBN 80-01-01860-1.
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P. Vodstrčil, J. Bouchala. Integrální počet funkcí více proměnných. 2012.
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