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

Course Unit Code | 310-3141/01 | |||||
---|---|---|---|---|---|---|

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 | ||||

KUC14 | prof. RNDr. Radek Kučera, Ph.D. | |||||

KRC76 | Mgr. Jiří Krček | |||||

Summary | ||||||

Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions, Euler method for homogeneous systems of n equations for n functions. Integral calculus of functions of several independent variables: two-dimensional integrals, three-dimensional integrals, vector analysis, line integral of the first and the second kind, surface integral of the first and second kind. | ||||||

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

The aim of the subject is to extend the mathematical topics from the bachelor study. Students will become familiar with systems of linear differential equations, double, triple, curve, and surface integrals and with basic concepts from field theory. | ||||||

Course Contents | ||||||

1 Systems of n ordinary linear differential equations of the first order for n functions: definition, representation at matrix form, methods of solution of systems of 2 equations for 2 functions.
2 Euler method for homogeneous systems of n equations for n functions. 3 Variation of constants. 4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2. 5 Transformation - polar coordinates, geometrical and physical applications. 6 Three-dimensional integrals on coordinate cube, on bounded subset of R3. 7 Transformation - cylindrical and spherical coordinates, geometrical and physical applications. 8 Vector analysis, gradient. 9 Divergence, rotation. 10 Line integral of the first and of the second kind. 11 Green´s theorem, potential. 12 Geometrical and physical applications. 13 Surface integral of the first and of the second kind. 14 Stokes and Gauss-Ostrogradski theorem. | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990. ISBN 0-669-21145-1
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 | ||||||

[1] Burda, P., Doležalová, J.: Integrální počet funkcí více proměnných – Matematika IIIb. Skriptum VŠB-TUO, Ostrava, 2003. ISBN 80-248-0454-9
[2] Burda, P., Doležalová, J.: Cvičení z matematiky IV. Skriptum VŠB-TUO, Ostrava, 2002. ISBN 80-248-0028-4 [3] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990. ISBN 0-669-21145-1 [4] http://www.studopory.vsb.cz | ||||||

Recommended Reading: | ||||||

[1] Harshbarger, R., J., Reynolds, J., J.: Calculus with Applications. D. C. Heath and Company, Lexington1990, ISBN 0-669-21145-1
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 | ||||||

[1] Škrášek, J., Tichý, Z.: Základy aplikované matematiky II. SNTL Praha, 1986
[2] James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 [3] http://mdg.vsb.cz/M | ||||||

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

Lectures, Individual consultations, Tutorials, Other activities | ||||||

Assesment methods and criteria | ||||||

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

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

Credit | Credit | 20 | 5 | |||

Examination | Examination | 80 (80) | 30 | |||

Praktická část | Written examination | 60 | 25 | |||

Teoretická část | Written examination | 20 | 5 |