| Course Unit Code | 714-0566/01 |
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| Number of ECTS Credits Allocated | 5 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 | Summer 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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| 714-0565 | Basics of Mathematics |
| Name of Lecturer(s) | Personal ID | Name |
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| DLO44 | Mgr. Dagmar Dlouhá, Ph.D. |
| DUB02 | RNDr. Viktor Dubovský, Ph.D. |
| VOL18 | RNDr. Jana Volná, Ph.D. |
| URB0186 | RNDr. Zbyněk Urban, Ph.D. |
| Summary |
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| The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three basic parts of mathematics, according to which the learning material is structured. In Differential Calculus, the main motive is the preparation to general use of derivatives of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Analytic geometry, there are, based on vector calculus, described basic linear formations of three-dimensional Euclidean space and some tools to evaluate their mutual position from qualitative and also quantitative point of view. |
| 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 toanalyze 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 , 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, Taylor polynom, parametric differentiation, highes-order derivative, L'Hospital rule
7 Applications of the derivatives, convexity and concavity of a function
8 Extremes of function, asmptotes, function graph constructing
9 Linear algebra: Vectors, linear independence. Matrices (basic properties)
10 Determinants (basic properties, calculation, evaluation)
11 Rank of matrix, matrix inversion
12 Systems of linear equations, Frobenius theorem, Gaussian elimination
13 Products of vectors (basic properties)
14 Line and plane equation in E3, mutual positions of lines and planes
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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 |
Burda, P., Havelek, R., Hradecká, R., Kreml.P: Matematika I, Učební texty VŠB-TU Ostrava, ISBN 978-80-248-1296-0, www.studopory.vsb.cz
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| Recommended Reading: |
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Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1
Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1 |
Škrášek, J. a kol.: Základy aplikované matematiky I. a II. SNTL, Praha 1989, IISBN 04-0544-89
Burda, P., Kreml, P.: Diferenciální počet funkcí jedné proměnné. Matematika
IIa. Učební texty VŠB - TUO, 2004, ISBN 80-248--0634-7
Burda, P., Havelek, R., Hradecká, R.: Algebra a analytická geometrie.
Matematika I. Učební texty VŠB - TUO, 1997, ISBN 80-7078-479-2 |
| Planned learning activities and teaching methods |
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| Lectures, Individual consultations, Tutorials |
| 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) | 30 |
| Written examination | Written examination | 60 | 25 |
| Oral | Oral examination | 20 | 5 |