* Exchange students do not have to consider this information when selecting suitable courses for an exchange stay.

Course Unit Code | 714-0015/01 | |||||
---|---|---|---|---|---|---|

Number of ECTS Credits Allocated | 5 ECTS credits | |||||

Type of Course Unit * | Compulsory | |||||

Level of Course Unit * | Second Cycle | |||||

Year of Study * | First Year | |||||

Semester when the Course Unit is delivered | Winter Semester | |||||

Mode of Delivery | Face-to-face | |||||

Language of Instruction | Czech | |||||

Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit | |||||

Name of Lecturer(s) | Personal ID | Name | ||||

STR78 | Mgr. Jakub Stryja, Ph.D. | |||||

Summary | ||||||

Double and triple integrals and their applications. Line integral and its
applications. Infinite series, power series. | ||||||

Learning Outcomes of the Course Unit | ||||||

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 | ||||||

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, Lebniz test. 11. Power series - convergency interval, radius of convergence, sum of a powerseries. 12. Taylor expansion, applications. | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1
| ||||||

http://www.studopory.vsb.cz/
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.: Řady – Matematika VI. Skriptum VŠB-TU, Ostrava 2000. ISBN 80-7078-775-9. | ||||||

Recommended Reading: | ||||||

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
mdg.vsb.cz/M/ | ||||||

Planned learning activities and teaching methods | ||||||

Lectures, Tutorials, Project work | ||||||

Assesment methods and criteria | ||||||

Task Title | Task Type | Maximum Number of Points (Act. for Subtasks) | Minimum Number of Points for Task Passing | |||

Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 | |||

Exercises evaluation | Credit | 20 | 10 | |||

Examination | Examination | 80 (80) | 31 | |||

Písemná zkouška | Written examination | 60 | 25 | |||

Ústní zkouška | Oral examination | 20 | 5 |