Course Unit Code | 230-0304/01 |
---|
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/
http://mdg.vsb.cz/portal/m4
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, Individual consultations, Tutorials |
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 | 10 |
Examination | Examination | 80 (80) | 30 |
Písemná zkouška | Written examination | 60 | 25 |
Ústní zkouška | Oral examination | 20 | 5 |