| Course Unit Code | 470-2101/03 |
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| Number of ECTS Credits Allocated | 2 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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| JAH02 | RNDr. Pavel Jahoda, Ph.D. |
| Summary |
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| Precalculus is an advanced form of secondary school algebra. Precalculus are intended to prepare students for the study of calculus and includes a review of algebra and trigonometry, as well as an introduction to exponential, logarithmic and trigonometric functions, vectors, complex numbers and analytic geometry. |
| Learning Outcomes of the Course Unit |
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Student gets the bysic knowledges and skills which are neresary for further studies at VSB-TUO during the course.
Students are able to evaluate the truth value of the logical statement, explain the difference between the basic numeric sets, edit the algebraic expression to describe the properties of functions, their domains, to quantify the functional values of elementary functions in the notable points and draw the graphs of these functions. In addition, the student is able to solve linear, quadratic, exponential, logarithmic and trigonometric equations and inequalities and to use this skills to solve elementary problems of analytic geometry.
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| Course Contents |
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Syllabus of lectures:
- Sets. Mathematical induction.
- Rational numbes. Which numbers have rational square roots? What is a real number? Complex numbers.
- The formal rules of algebra. Completing the square. Solving a quadratic equation by completing the square. The quadratic formula. Synthetic division by x − a. The fundamental theorem of algebra.
- Functions. What is a function? Functional notation. A function of a function. The graph of a function. Coördinate pairs of a function. Odd and even functions.
- Basic graphs. The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function. Translations of a graph.
- Linear functions. The graph of a first degree equation -- a straight line. Polynomials of the second degree. Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots.
- Polynomial functions. Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial. The roots, or zeros, of a polynomial. The polynomial equation. The roots of a polynomial.
- The slope of a straight line. Definition of the slope. Positive and negative slope. A straight line has only one slope. Perpendicular lines.
- Rational functions.
- Inverse functions. Definition of inverses. Constructing the inverse. The graph of an inverse function.
- Logarithmic and exponential functions.
Logarithms.The system of common logarithms. The system of natural logarithms. The three laws of logarithms. Change of base.
- Trigonometric functions.
- Analytic geometry. |
| Recommended or Required Reading |
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| Required Reading: |
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R. G. Brown, D. P. Robbins: Advanced Mathematics (A Precalculus Course), Houghton Mifflin Comp., Boston 1989.
Libor Šindel: Principles of mathematics (The text is in electronic form). |
J. Polák, Přehled středoškolské matematiky, Prometheus, ISBN 80-85849-78-X
J. Polák, Středoškolská matematika v úlohách I, Prometheus.
J. Polák, Středoškolská matematika v úlohách II, Prometheus.
B. Budinský, J. Charvát: Matematika I, SNTL Praha 1987, ISBN 04-011-87.
R. G. Brown, D. P. Robbins: Advanced Mathematics (A Precalculus Course), Houghton Mifflin Comp., Boston 1989. |
| Recommended Reading: |
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| Richard G. Brown, David P. Robbins, Advanced Mathematics a precalculus course |
J. Kuben, P. Šarmanová, Diferenciální počet funkcí jedné proměnné, multimediální výukové CD, VŠB-TU Ostrava, 2006, http://www.am.vsb.cz/sarmanova/cd
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| Planned learning activities and teaching methods |
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| 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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| Credit | Credit | 30 | 10 |