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Lecturer(s)
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Hora Jaroslav, Doc. RNDr. CSc.
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Course content
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Content: 1st ? 2nd week: Physical application of definite integral (geometric center of object, moment of inertia, etc.). 3rd week: Function with multiple arguments. 4th week: Limits and continuity of function with multiple arguments. 5th week: Partial derivation and its geometric significance. 6th week: Total differential, its geometric significance, total derivative theorems, calculations. 7th week: Differentiation of composite function. 8th week: Higher order differentials. 9th - 10th week: Extremes of functions with multiple arguments. 11th ? 13th week: Double integral, its geometric significance, examples.
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Learning activities and teaching methods
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Lecture, Seminar
- Preparation for comprehensive test (10-40)
- 20 hours per semester
- Contact hours
- 39 hours per semester
- Preparation for formative assessments (2-20)
- 20 hours per semester
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| prerequisite |
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| Knowledge |
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| Assumptions Knowledge of elementary methods of differential and integral calculus is assumed. No prerequisites. |
| learning outcomes |
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| Learning outcomes and gained competencies: Student ? can define domain and range of complicated function, - knows common methods known from theory of one real variable functions, - masters especially methods for finding function limits and derivatives, - knows elementary integration techniques, - can apply integrations for counting area of plane geometric object, volume of rotating physical body, length of curve, etc., - understands the connection to school geometry, - understands the principles of analytic expression of linear object, curves and elementary surfaces, expresses concrete linear object with an equation. Especially learning, communicative, problem-solving and professional competences are bein developed. |
| teaching methods |
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| Lecture |
| Seminar |
| assessment methods |
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| Test |
| Seminar work |
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Recommended literature
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Jarník, Vojtěch. Integrální počet. II. Praha : Nakladatelství Československé akademie věd, 1955.
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KOUTKOVÁ, H., PRUDILOVÁ, K. Sbírka příkladů z matematiky III: modul BA02-M05: dvojný, trojný a křivkový integrál. Brno: Akademické nakladatelství CERM, 2019. ISBN 978-80-7623-011-8.
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KRBÁLEK, M. Funkce více proměnných. Praha: České vysoké učení technické, 2021. ISBN 978-80-01-06837-3.
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