| Course Unit Code | 470-2111/07 |
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| Number of ECTS Credits Allocated | 8 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | First Year |
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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 | 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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| BOU10 | prof. RNDr. Jiří Bouchala, Ph.D. |
| 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.
- Taylor's theorem.
- Extremes of more-variable real functions.
- Definition of double integral, basic properties. Fubini theorems for
double integral.
- Transformation of double integral, aplications of double integral.
- Definition of triple integral, basic properties. Fubini theorems for triple
integral.
- Transformation of triple integral, aplications of triple integral.
Exercises:
- More-variable real functions. Partial and directional derivatives,
differential and gradient.
- Taylor's theorem.
- Extremes of more-variable real functions.
- Definition of double integral, basic properties. Fubini theorems for double
integral.
- Transformation of double integral, aplications of double integral.
- Definition of triple integral, basic properties. Fubini theorems for triple
integral.
- Transformation of triple integral, aplications of triple integral.
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| Recommended or Required Reading |
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| Required Reading: |
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BOUCHALA, Jiří; KRAJC, Bohumil. Introduction to Differential Calculus of Several Variables, 2022
http://am.vsb.cz/bouchala
BOUCHALA, Jiří; VODSTRČIL, Petr; ULČÁK, David. Integral Calculus of Multivariate
Functions, 2022
http://am.vsb.cz/bouchala
|
BOUCHALA, Jiří. Matematická analýza II. Ostrava: VŠB - Technická univerzita Ostrava, 2007. ISBN 978-80-248-1587-9.
BOUCHALA, Jiří; VODSTRČIL, Petr. Integrální počet funkcí více proměnných, 2012
http://mi21.vsb.cz/modul/integralni-pocet-funkci-vice-promennych
BOUCHALA, Jiří; KRAJC, Bohumil. Introduction to Differential Calculus of Several Variables, 2022
http://am.vsb.cz/bouchala
BOUCHALA, Jiří; VODSTRČIL, Petr; ULČÁK, David. Integral Calculus of Multivariate
Functions, 2022
http://am.vsb.cz/bouchala
|
| Recommended Reading: |
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| ANTON, Howard; BIVENS, Irl a DAVIS, Stephen. Calculus. 8th ed. Hoboken: Wiley, c2005. ISBN 0-471-48273-0. |
ZAJÍČEK, Luděk. Vybrané partie z matematické analýzy pro 1. a 2. ročník. Praha: Matfyzpress, 2003. ISBN 80-86732-09-6.
REKTORYS, Karel. Přehled užité matematiky I. 7. vyd. Česká matice technická, č. spisu 487, roč. 100 (2000). Praha: Prometheus, 2000. ISBN 80-7196-180-9.
REKTORYS, Karel. Přehled užité matematiky II. 7. vyd. Česká matice technická, č. spisu 487, roč. 100 (2000). Praha: Prometheus, 2000. ISBN 80-7196-181-7.
ANTON, Howard; BIVENS, Irl a DAVIS, Stephen. Calculus. 8th ed. Hoboken: Wiley, c2005. ISBN 0-471-48273-0. |
| 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 |