| Course Unit Code | 310-2117/01 |
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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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| KOT31 | RNDr. Jan Kotůlek, Ph.D. |
| JAH0037 | Mgr. Monika Jahodová, Ph.D. |
| MUL0086 | RNDr. PhDr. Ivo Müller, Ph.D. |
| Summary |
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The subject is divided into four chapters.
In the first chapter we study real functions of one real variable and their properties, in the second chapter we introduce the notion of derivative and study its properties and applications.
In the third chapter we introduce Gauss elimination method for solution of systems of linear algebraic equations. In the last chapter we apply it to the geometric problems in three-dimensional Euclidean space.
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| Learning Outcomes of the Course Unit |
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Mathematics is an essential part of the engineering programmes. Nevertheless, it is not a a goal on its own, but rather a necessary tool for understanding the technical subjects.
Therefore, we aim to both introducing the basic mathematical concepts and deepen the logical and analytical thinking of our students.
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| Course Contents |
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1. Functions of one real variable (definitions and basic properties).
2. Elementary functions. Parametric and implicit functions.
3. Limit of the function, continuous functions. Definition of the derivative.
4-5. Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
6-8. Applications of the derivatives. Tangent line, Taylor polynomial, extremes of a function. Behaviour of the graph. Monotonic functions. Convex and concave functions. Inverse functions. Computation of limits by l'Hospital rule. Asymptotes.
9. Systems of linear equations, Gaussian elimination
10. Matrices, rank of a matrix. Matrix inversion
11. Determinant, its computation and properties. Cramer rule.
12. Analytic geometry in Euclidean space. Dot product and cross product
13. Line and plane in 3D-Euclidean space.
14. Mutual positions and metric properties of subspaces in 3D-Euclidean space.
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| Recommended or Required Reading |
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| Required Reading: |
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BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1.
NEUSTUPA, Jiří. Mathematics. 2. Vyd. Praha: Vydavatelství ČVUT, 2004. ISBN 80-01-02946-8.
BĚLOHLÁVKOVÁ, Jana, Jan KOTŮLEK, Worksheets for Mathematics I. 1. vyd. Ostrava: VŠB-TUO, 2020.
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DLOUHÁ, Dagmar, Radka HAMŘÍKOVÁ, Zuzana MORÁVKOVÁ a Michaela BOBKOVÁ. Matematika I: Pracovní listy. Ostrava: VŠB-TUO, 2014. ISBN 978-80-248-3323-1.
VRBENSKÁ, Helena a Jana BĚLOHLÁVKOVÁ. Základy matematiky pro bakaláře I. 3. vyd. Ostrava: VŠB - Technická univerzita Ostrava, 2009. ISBN 80-248-0519-7.
HAMŘÍKOVÁ, R.: Sbírka úloh z matematiky. Ostrava: VŠB-TUO, 2007. ISBN 978-80-248-1299-1.
BURDA, Pavel, Radim HAVELEK, Radoslava HRADECKÁ a Pavel KREML. Matematika I. Ostrava: VŠB-TUO, 2007. ISBN 80-248-1199-5
Vše online na URL: http://mdg.vsb.cz/portal/
BIRD, J. O. Higher engineering mathematics. Eighth edition. London: Routledge, Taylor & Francis Group, 2017. ISBN 978-1-138-67357-1.
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| Recommended Reading: |
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ANDREESCU, Titu. Essential linear algebra with applications: a problem-solving approach. New York: Birkhäuser, [2014]. ISBN 978-0-8176-4360-7.
HARSHBARGER, Ronald J. a REYNOLDS, James J. Calculus with applications. 2nd ed. Lexington: D.C. Heath, 1993. xiv, 592 s. ISBN 0-669-33162-7.
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
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MUSILOVÁ, Jana a Pavla MUSILOVÁ. Matematika I: pro porozumění i praxi. 2., dopl. vyd. Brno: VUTIUM, 2009. ISBN 978-80-214-3631-2.
ŠKRÁŠEK, Josef a Zdeněk TICHÝ. Základy aplikované matematiky I: matematická logika, množiny, základy algebry, analytická geometrie, diferenciální počet, numerické a grafické metody. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1989.
STRANG, Gilbert. Calculus. 3. vyd. Wellesley, MA: Wellesley-Cambridge Press, 2017. ISBN 978-0-9802327-5-2.
ANDREESCU, Titu. Essential linear algebra with applications: a problem-solving approach. New York: Birkhäuser, [2014]. ISBN 978-0-8176-4360-7.
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| 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 | 5 |
| Examination | Examination | 80 (80) | 30 |
| Computing of the derivatives | Written test | | |
| Practical part | Written examination | 60 | 25 |
| Theoretical part | Written test | 20 | 5 |