| Course Unit Code | 470-4116/02 |
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| Number of ECTS Credits Allocated | 5 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| KRA04 | Mgr. Bohumil Krajc, Ph.D. |
| S1A64 | RNDr. Petra Vondráková, Ph.D. |
| Summary |
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This subject contains 3 basic topics:
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differential calculus in two and more-variables,
integral calculus in more-variables,
differential equations.
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| Learning Outcomes of the Course Unit |
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Students will learn about differential calculus of more-variable real functions.
In the second part students will get the basic practical skills for working with fundamental concepts, methods and applications of integral calculus of more-variable real functions.
In the last part of this subject students will be able to solve differential equations. |
| Course Contents |
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More-variable real functions. Partial and directional derivatives, differential and gradient.
Taylor's theorem.
Extremes of more-variable real functions.
Definition of Riemann double integral, basic properties. Fubini theorems for double integral.
Transformation of double integral, aplications of double integral.
Definition of Riemann triple integral, basic properties. Fubini theorems for triple integral.
Transformation of triple integral, aplications of triple integral.
Linear differential equations. |
| Recommended or Required Reading |
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| Required Reading: |
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| J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO. |
J. Bouchala: Matematika III, www.am.vsb.cz/bouchala, 2000.
P. Vodstrčil, J. Bouchala: Integrální počet funkcí více proměnných, http://mi21.vsb.cz/modul/integralni-pocet-funkci-vice-promennych , 2012.
J. Brabec, B. Hrůza: Matematická analýza II, SNTL, Praha, 1986.
B. Budinský, J. Charvát: Matematika II, SNTL, Praha, 1990.
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| Recommended Reading: |
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| L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973. |
J. Bouchala: Matematická analýza 1, skripta VŠB-TUO, 2000.
J. Bouchala: Sbírka příkladů z matematické analýzy 1, 2 a 3, www.am.vsb.cz/bouchala.
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| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 (30) | 10 |
| 1. zápočtový test | Written test | 12 | 0 |
| 2. zápočtový test | Written test | 12 | 0 |
| Projekt | Project | 6 | 0 |
| Examination | Examination | 70 | 21 |