| Course Unit Code | 470-2111/06 |
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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 * | First Cycle |
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| Year of Study * | |
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| Semester when the Course Unit is delivered | Summer Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | English |
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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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| KRA04 | Mgr. Bohumil Krajc, Ph.D. |
| Summary |
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This subject contains following topics:
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differential calculus of two and more-variable real functions,
integral calculus of more-variable real functions or differential equations (according to the version) |
| 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.
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| Course Contents |
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Lectures:
More-variable real functions
Partial and directional derivatives
Differential and gradient, tangent plane and linear approximations
Taylor's theorem
Extremes of more-variable real functions
Differential equations
Separable equations
Linear equations
Second order linear equations
Applications of first-order and second-order differentials equations
Exercises:
More-variable real functions - domain, level curves, graphs
Partial and directional derivatives
Differential and gradient, tangent plane and linear approximations
Taylor's theorem
Extremes of more-variable real functions
Differential equations. Separable equations
Linear equations
Second order linear equations
Applications of first-order and second-order differentials equations |
| Recommended or Required Reading |
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| Required Reading: |
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| L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973. |
J. Bouchala: Matematika III, www.am.vsb.cz/bouchala, 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.
P. Vodstrčil, J. Bouchala: Integrální počet funkcí více proměnných
(http://mi21.vsb.cz/modul/integralni-pocet-funkci-vice-promennych), 2012.
B. Krajc, P. Beremlijski: Obyčejné diferenciální rovnice (http://mi21.vsb.cz/modul/obycejne-diferencialni-rovnice), 2012.
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
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| Recommended Reading: |
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| J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO. |
J. Bouchala: Sbírka příkladů z matematické analýzy 1, 2 a 3, www.am.vsb.cz/bouchala.
J. Brabec, B. Hrůza: Matematická analýza II, SNTL, Praha, 1986.
B. Budinský, J. Charvát: Matematika II, SNTL, Praha, 1990.
L. Gillman, R. H. McDowell: Calculus, New York, W.W. Norton & Comp. Inc. 1973.
J. Bouchala, M. Sadowská: Mathematical Analysis I, VŠB-TUO. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| Assesment methods and criteria |
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| Tasks are not Defined |