| Course Unit Code | 470-4121/01 |
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| Number of ECTS Credits Allocated | 4 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second 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 | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| VOD03 | doc. Mgr. Petr Vodstrčil, Ph.D. |
| Summary |
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This subject contains the following themes:
- more-variable functions, extremes
- function spaces
- functionals and their extremes
- applications |
| Learning Outcomes of the Course Unit |
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| After completing the course the student will be able to work with more-variable real functions. He will be able to find extremes of such functions. In addition, the student will be able to calculate the derivative of functionals and also seek their extremes. |
| Course Contents |
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Lectures:
- more-variable functions, partial derivatives, Schwarz theorem
- gradient
- relative extremes
- extremum problems with constraints
- absolute extremes
- numerical methods
- linear spaces, norm linear spaces
- function spaces, functionals
- derivative of functional
- extremes of functionals, Euler-Lagrange equation
- applications
Exercises:
- more-variable functions, partial derivatives, Schwarz theorem
- gradient
- relative extremes
- extremum problems with constraints
- absolute extremes
- numerical methods
- linear spaces, norm linear spaces
- function spaces, functionals
- derivative of functional
- extremes of functionals, Euler-Lagrange equation
- applications
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| Recommended or Required Reading |
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| Required Reading: |
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H. Anton, I. Bivens, S. Davis: Calculus, 2009
L.E. Elsgolc: Calculus of Variations, 2007 |
J. Bouchala: Matematika III, http://homel.vsb.cz/~bou10/archiv/ma3_bc.pdf , 2000.
O. Došlý: Variační počet, http://www.math.muni.cz/~dosly/varpoc.pdf
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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. Kuben, Š. Mayerová, P. Račková, P. Šarmanová: Diferenciální počet funkcí více proměnných, http://mi21.vsb.cz/modul/diferencialni-pocet-funkci-vice-promennych , 2012.
L.E. Elsgolc: Variační počet.
P. Vodstrčil, J. Bouchala: Integrální počet funkcí více proměnných, http://mi21.vsb.cz/modul/integralni-pocet-funkci-vice-promennych , 2012. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| 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 | 10 |
| Examination | Examination | 70 | 21 |