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Mathematics I

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

Course Unit Code310-2211/01
Number of ECTS Credits Allocated7 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First 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
MOR74Mgr. Zuzana Morávková, Ph.D.
Summary
Differential calculus of function of one real independent variable: function of one variable, elementary functions, limit and continuity of a function, differentiation, extreme values of function, point of inflection, convex and concave function, L’Hospital’s rule.
Linear algebra: determinants, matrices, systems of linear equations.
Analytic geometry of the 3-dimensional space.

Learning Outcomes of the Course Unit
The goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithmus and methods. Students should learn how to
analyze problem,suggest a method of solution, analyze correctness of achieved results with respect to given conditions.
Course Contents
1 Functions of one real variable (definitions and basic properties)
2 Elementary functions
3 Limit of the function, continuity of the functions , basic rules
4 Differential calculus functions of one real variable. the derivative of function (basic rules for differentiation)
5 Derivatives of selected functions
6 Differential of the function, parametric differentiation, highes-order derivative
7 Applications of the derivatives
8 Monotonic functions and extremes of function, convexity and concavity of a function
9 Linear algebra: Matrice (basic properties), determinants (basic properties, calculation, evaluation)
10 Matrix inversion
11 Systems of linear equations, Cramer’s rule
12 Gaussian elimination
13 Product of vectors (basic properties)
14 Analytical geometry in E3

Recommended or Required Reading
Required Reading:
[1] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3, http://mdg.vsb.cz/portal/en/Mathematics1.pdf
[2] BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1
[3] TRENCH, W.F.: Introduction to real analysis, Free Edition 1.06, January 2011,ISBN 0-13-045786-8
[1] BURDA, P. a kol: Matematika I. Skriptum VŠB–TUO, Ostrava 2007. ISBN 80-248-1199-5
[2] BURDA,P.: Algebra a analytická geometrie. Skriptum VŠB-TU, Ostrava 1997. ISBN 80-7078-479-2
[3] DLOUHÁ, D., HAMŘÍKOVÁ, R., MORÁVKOVÁ, Z. a M. BOBKOVÁ. Matematika I: Pracovní listy. Ostrava: VŠB - Technická univerzita Ostrava, 2014. ISBN 978-80-248-3323-1
Recommended Reading:
[1] James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6
[1] Vrbenská, H., Němčíková, J.: Základy matematiky pro bakaláře I. Skriptum VŠB-TUO, Ostrava 1999. ISBN 80-7078-351-6
[2] Vrbenská, H., Bělohlávková, J.: Základy matematiky pro bakaláře II. Skriptum VŠB-TUO, Ostrava 1998. ISBN 80-7078-545-4
Planned learning activities and teaching methods
Lectures, Individual consultations, Tutorials, Other activities
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
Credit and ExaminationCredit and Examination100 (100)51
        CreditCredit20 5
        ExaminationExamination80 (80)30
                písemkaWritten test60 25
                teorieOral examination20 5