| Course Unit Code | 714-0068/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | First Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | There are no prerequisites or co-requisites for this course unit |
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| Name of Lecturer(s) | Personal ID | Name |
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| KRA44 | Mgr. Kateřina Kozlová, Ph.D. |
| Summary |
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The functions of one real variable, the derivation of a
function of one variable. Derivations of higher orders. Investigating the
behaviour of functions. Antiderivative and the indefinite integral, some
properties, elementary methods of integration. Linear algebra: Arithmetic
vectors, matrices, determinants, systems of linear algebraic equations.
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| Learning Outcomes of the Course Unit |
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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.
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| Course Contents |
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1 Functions of one real variable (definitions and basic properties)
2 Elementary functions
3 Limit of the function, continuity of the functions.
4 Differential calculus functions of one real variable. Geometrical and physical meaning, basic rules for differentiation.
5 Derivatives of selected functions
6 Differential of the function, parametric differentiation, highes-order derivative, L´Hospital´s rule.
7 Applications of the derivatives. Monotonic functions and extremes of a function, convexity and concavity of a function.
8 Asymptotes, constructing graphs.
9 Linear algebra. Arithmetic vectors, linear dependence and linear independence of vectors. Matrix (basic properties), rank of a matrix.
10 Determinants. Basic properties, calculation, evaluation.
11 System of linear equations, Cramer’s rule, Gaussian elimination algorithm. Matrix inversion.
12 Analytical geometry in E3. Geometrical vector, basic operations. Inner product, cross product and applications.
13 Plane and line in E3, metric problems.
14 Reserve.
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| Recommended or Required Reading |
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| Required Reading: |
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| Doležalová, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3 |
[1] Burda, P.-Kreml, P.: Diferenciální počet funkcí jedné proměnné. Skriptum
VŠB, Ostrava 2004. ISBN 80-248-0634-7
[2] Burda,P.: Algebra a analytická geometrie. Skripta VŠB-TU, Ostrava 1997.
ISBN 80-7078-479-2
[3] Vrbenská, H., Němčíková, J.: Základy matematiky pro bakaláře I. Skriptum
VŠB-TUO, Ostrava 1999. ISBN 80-7078-351-6
[4] Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II.
Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
[5] www.studopory.vsb.cz |
| Recommended Reading: |
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[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
[3] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6
|
[1] Škrášek, J., Tichý,Z.: Základy aplikované matematiky I. SNTL, Praha 1990.
[2] Rektorys, K.: Co je a k čemu je vyšší matematika. ACADEMIA, Praha 2001.
ISBN 80-200-0883-7
[3] http://mdg.vsb.cz/M |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials, Other activities |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 20 | 10 |
| Examination | Examination | 80 (80) | 30 |
| Písemná část | Written test | 60 | 25 |
| Ústni část | Oral examination | 20 | 5 |