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

Course Unit Code | 714-0369/01 | |||||
---|---|---|---|---|---|---|

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, English | |||||

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

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

DOL30 | doc. RNDr. Jarmila Doležalová, CSc. | |||||

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. Infinite series: number series, series of functions, power series. | ||||||

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

Mathematics is essential part of education on technical universities.
It should be considered rather the method in the study of technical courses than a goal. Thus 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, verify each step of a method, generalize achieved results, analyze correctness of achieved results with respect to given conditions, apply these methods while solving technical problems, understand that mathematical methods and theoretical advancements outreach the field mathematics. | ||||||

Course Contents | ||||||

Syllabus of lecture
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 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2 4 Transformation - polar coordinates, geometrical and physical applications 5 Three-dimensional integrals on coordinate cube, on bounded subset of R3 6 Transformation - cylindrical and spherical coordinates, geometrical and physical applications 7 Vector analysis, gradient 8 Divergence, rotation 9 Line integral of the first and of the second kind 10 Green´s theorem, potential 11 Geometrical and physical applications 12 Infinite number series 13 Infinite series of functions, power series Syllabus of tutorial 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 Euler method for homogeneous systems of n equations for n functions, test 4 Integral calculus of functions of several independent variables: two-dimensional integrals on coordinate rectangle, on bounded subset of R2 5 Transformation - polar coordinates 6 Geometrical and physical applications 7 Three-dimensional integrals on coordinate cube, on bounded subset of R3 8 Transformation - cylindrical and spherical coordinates 9 Geometrical and physical applications, test 10 Vector analysis, gradient 11 Divergence, rotation 12 Line integral of the first kind 13 Line integral of the second kind, test 14 Geometrical and physical applications | ||||||

Recommended or Required Reading | ||||||

Required Reading: | ||||||

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

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, R.J.-Reynolds, J.J.: Calculus with Applications.
D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456 James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6 | ||||||

Častová, N. a kol.: Cvičení z matematiky III. Skriptum VŠB, Ostrava 1988
Škrášek, J.-Tichý, Z.: Základy aplikované matematiky II. SNTL Praha, 1986 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 | |||

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

Exercises evaluation | Credit | 20 | 5 | |||

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

written exam | Written examination | 60 | 25 | |||

Oral examination | Oral examination | 20 | 5 |