| Course Unit Code | 714-0565/05 |
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| Number of ECTS Credits Allocated | 1 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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| DLO44 | Mgr. Dagmar Dlouhá, Ph.D. |
| DUB02 | RNDr. Viktor Dubovský, Ph.D. |
| SKA141 | Mgr. Pavel Skalný, Ph.D. |
| URB0186 | RNDr. Zbyněk Urban, Ph.D. |
| Summary |
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The set of real numbers, operations with algebraic expressions, equations and
inequalities, functions, exponential and logarithmic equations, trigonometric
functions and equations, analytic geometry, arithmetic and geometric sequences. |
| 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. |
| Course Contents |
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Week. Tutorial
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1st Functions: properties, domain, linear, quadratic, cubic, irrational and rational functions.
2nd Exponential and logarithmic functions. Evaluation of logarithms. Exponential equations and inequalities.
3rd Goniometric functions, their graphs and values. Trigonometric equations and inequalities.
4th Mathematical logic: constants, variables, statements and operations.
5th Set theory: types of sets, operations with sets, sets of numbers, intervals.
6th Algebraic expressions: polynomials, fractions, powers, roots.
7th Equations: linear, linear with parameters, quadratic, irrational, systems of two linear equations.
8th Inequalities: linear, quadratic, systems.
9th Absolutní value: geometric interpretation, equations and inequalities.
10th Basics of analytical geometry: vectors, lines, circle, determination of the center and radius.
11th Elipsis, hyperbole, parabole: determination of parameters.
12th Sequences and series.
13th Complex numbers.
14th Tests and credits.
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| Recommended or Required Reading |
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| Required Reading: |
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| [1] Harshbarger, R.J. - Teynolds, J.J.: Calculus with Applications. D.C. Heath and Company, Lexington 1990, ISBN 0-669-21145-1 |
[1] Boháč, Z.-Burda, P.-Doležalová, J.: Matematika pro přípravný kurz a přijímací zkoušku na VŠB - TU. Skriptum VŠB - TU, Ostrava 2003. ISBN 80-7078-278-1
[2] Polák, J.: Přehled středoškolské matematiky. SPN, Praha 1991. ISBN 80-7196-267-8
[3] Polák, J.: Středoškolská matematika v úlohách I. Prometheus, Praha 1996. ISBN 80-7196-021-7
[4]www.studopory.vsb.cz |
| Recommended Reading: |
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Basic textbooks on mathematics.
http://mdg.vsb.cz/M |
Středoškolské učebnice matematiky.
http://mdg.vsb.cz/M |
| Planned learning activities and teaching methods |
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| 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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| Graded exercises evaluation | Graded credit | 100 (100) | 51 |
| písemka | Written test | 100 | 51 |