| Course Unit Code | 714-0366/03 |
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| Number of ECTS Credits Allocated | 4 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 | |
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| Prerequisities | Course Unit Code | Course Unit Title |
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| 714-0365 | Basics of Mathematics |
| Name of Lecturer(s) | Personal ID | Name |
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| H1O40 | Mgr. Iveta Cholevová, Ph.D. |
| ZID76 | Mgr. Arnošt Žídek, Ph.D. |
| KOT31 | RNDr. Jan Kotůlek, Ph.D. |
| JAH0037 | Mgr. Monika Jahodová, 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 study linear algebra. 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. |
| 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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Syllabus of lectures
1 Functions of one real variable (definitions and basic properties). Inverse functions.
2 Elementary functions. Parametric and implicit functions.
3 Limit of the function, continuous functions.
4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
5 Applications of the derivatives, l'Hospital rule. Taylor polynomial.
6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions.
7 Asymptotes. Constructing graph of a function.
8 Linear algebra. Vector spaces, bases, dimension.
9 Matrices, rank of a matrix.
10 Determinant. Matrix inversion.
11 Systems of linear equations, Gaussian elimination.
12 Analytic geometry in Euclidean space. Dot product and cross product.
13 Line and plane in 3D-Euclidean space.
14 Reserve.
Syllabus of tutorials
1 Functions of one real variable (definitions and basic properties). Inverse functions.
2 Elementary functions. Parametric and implicit functions.
3 Limit of the function, continuous functions.
4 Differential calculus functions of one real variable. Derivative (basic rules for differentiation). Parametric differentiation, higher-order derivatives.
5 Applications of the derivatives, l'Hospital rule. Taylor polynomial.
6 Applications of the derivatives on the behaviour of the graph. Monotonic functions. Convex and concave functions.
7 Asymptotes. Constructing graph of a function.
8 Linear algebra. Vector spaces, bases, dimension.
9 Matrices, rank of a matrix.
10 Determinant. Matrix inversion.
11 Systems of linear equations, Gaussian elimination.
12 Analytic geometry in Euclidean space. Dot product and cross product.
13 Line and plane in 3D-Euclidean space.
14 Reserve.
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| Recommended or Required Reading |
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| Required Reading: |
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[1] BIRD, J.: Engineering Mathematics, 4th ed. Newnes 2003.
[2] DOLEŽALOVÁ, J.: Mathematics I. VŠB – TUO, Ostrava 2005, ISBN 80-248-0796-3
[3] NEUSTUPA, J.: Mathematics I., ČVUT, Praha 2004
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DLOUHÁ, Dagmar, Radka HAMŘÍKOVÁ, Zuzana MORÁVKOVÁ a Michaela BOBKOVÁ. Matematika I: Pracovní listy. Ostrava: VŠB - Technická univerzita Ostrava, 2014. ISBN 978-80-248-3323-1.
Burda, P. a kol: Matematika I. Skriptum VŠB–TUO, Ostrava 2007. ISBN 80-248-1199-5.
http://www.studopory.vsb.cz/studijnimaterialy/MatematikaI/MI.html
Hamříková, R.: Sbírka úloh z matematiky. Skriptum VŠB–TUO, Ostrava 2007. ISBN 978-80-248-1317-2
http://www.studopory.vsb.cz/studijnimaterialy/Sbirka_uloh/
Vrbenská, H.: Základy matematiky pro bakaláře I. Skriptum VŠB - TU, Ostrava 1997. ISBN 80-7078-351-6. |
| Recommended Reading: |
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Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington 1990, ISBN 0-669-21145-1
James, G.: Modern Engineering Mathematics. Addison-Wesley, 1992. ISBN 0-201-1805456
James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6 |
Musilová J. - Musilová, P.: Matematika I pro porozumění i praxi (VUTIUM, Brno, 2006).
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1986.
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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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 20 | 5 |
| Examination | Examination | 80 (80) | 31 |
| Test z derivací | Written test | | |
| Praktická část | Written examination | 60 | 25 |
| Teoretická část | Oral examination | 20 | 5 |