| Course Unit Code | 230-0326/01 |
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| Number of ECTS Credits Allocated | 1 ECTS credits |
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| Type of Course Unit * | Choice-compulsory type B |
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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 | 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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| STR78 | Mgr. Jakub Stryja, Ph.D. |
| Summary |
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| Repetition of Engineering Mathematics is intended for students who, for whatever reasons, fail the exam of Engineering Mathematics and are interested in passing this exam. Its content essentially coincides with the content of the course Engineering Mathematics. Repetition will focus on the practical part of the exam. |
| Learning Outcomes of the Course Unit |
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The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to
analyze problems,
distinguish between important and unimportant,
suggest a method of solution and verify each step of an algorithm,
generalize achieved results,
analyze correctness of results with respect to given conditions,
apply these methods while solving technical problems. |
| Course Contents |
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1. Integral calculus of functions of several independent variables. Two-dimensional integrals on coordinate rectangle, on bounded subset of R2.
2. Transformation two-dimensional integrals, geometrical and physical applications.
3. Three-dimensional integrals on coordinate cube, on bounded subset of R3.
4. Transformation of three-dimensional integrals, geometrical and physical applications.
5. Line integral of the first and of the second kind.
6. Independence line integral on path, Green´s theorem.
7. Applications of line integrals.
8. Series. Infinite number series. Definition, sum of a series, necessary convergence condition, harmonic series, geometric series.
9. Convergency tests, ratio test, Cauchy's root test, comparison test, integral test.
10. Alternating series - absolute and conditional convergency, Leibniz test.
11. Power series - convergency interval, radius of convergence, sum of a powerseries.
12. Taylor expansion, applications. |
| Recommended or Required Reading |
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| Required Reading: |
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| Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1 |
Burda, P. - Doležalová, J.: Integrální počet funkcí více proměnných – Matematika IIIb. Skriptum VŠB, Ostrava 2003. ISBN 80-248-0454-9.
Burda, P. - Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB, Ostrava 2002. ISBN 80-248-0028-4.
Vlček, J. – Vrbický, J. - Stryja, J.: Řady. Skriptum VŠB-TU, Ostrava 2020. ISBN 978-80-248-4392-6, doi: https://doi.org/10.31490/9788024843926
http://mdg.vsb.cz/portal/m4
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| Recommended Reading: |
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Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992.
ISBN 0-201-1805456 |
| Škrášek, J.-Tichý, Z.: Základy aplikované matematiky I,II,III. SNTL, Praha 1986 |
| Planned learning activities and teaching methods |
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| 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 | Credit | | |