| Course Unit Code | 470-2111/12 |
|---|
| Number of ECTS Credits Allocated | 4 ECTS credits |
|---|
| Type of Course Unit * | Optional |
|---|
| Level of Course Unit * | First Cycle |
|---|
| Year of Study * | |
|---|
| Semester when the Course Unit is delivered | Winter Semester |
|---|
| Mode of Delivery | Face-to-face |
|---|
| Language of Instruction | English |
|---|
| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
|---|
| Name of Lecturer(s) | Personal ID | Name |
|---|
| KRA04 | Mgr. Bohumil Krajc, Ph.D. |
| LAM05 | prof. RNDr. Marek Lampart, Ph.D. |
| Summary |
|---|
This subject contains following topics:
-----------------------------------
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 |
|---|
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.
|
| Course Contents |
|---|
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.
|
| Recommended or Required Reading |
|---|
| Required Reading: |
|---|
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: |
|---|
| 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 |
|---|
| Lectures, Tutorials |
| Assesment methods and criteria |
|---|
| Tasks are not Defined |