Engineering Mathematics

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Course Unit Code714-0015/01
Number of ECTS Credits Allocated5 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *Second Cycle
Year of Study *First Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites There are no prerequisites or co-requisites for this course unit
Name of Lecturer(s)Personal IDName
STR78Mgr. 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 TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Exercises evaluation and ExaminationCredit and Examination100 (100)51
        Exercises evaluationCredit20 10
        ExaminationExamination80 (80)31
                Písemná zkouškaWritten examination60 25
                Ústní zkouškaOral examination20 5