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Lecturer(s)
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Krňávek Jan, Mgr. Ph.D.
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Polášek Vladimír, Mgr. Ph.D.
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Course content
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1. Fraction, square roots operations. Editing of algebraic expressions 2. Numerical operations with polynomials. Decomposition of a polynomial into the product of root factors. 3. Complete the square on a polynomial. Polynomial long division. Horner's method. 4. Basic elementary functions and their properties. Graph of a function. 5. Solution of selected types of equations and inequalities. 6. Vector space. Basic operations with vectors. 7. Linear dependence, independence of vectors. Scalar, vector product. 8. The notion of matrix and the special types of matrices, operations with matrices. 9. Row elementary operations, inverse matrix. 10. Determinant and operations with determinants. 11. Systems of linear equations - Gauss elimination. 12. Systems of linear equations - Cramer rule. 13. Analytic geometry in the plane. Point in the plane. General and parametric equation of a line. 14. Mutual position of lines in the plane. Deviation of straight lines in the plane. The distance of a point from a straight line in a plane.
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Learning activities and teaching methods
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Lecturing, Practice exercises, Individual work of students
- Preparation for course credit
- 60 hours per semester
- Participation in classes
- 42 hours per semester
- Home preparation for classes
- 33 hours per semester
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| prerequisite |
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| Knowledge |
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| Basic initial knowledge and skills of secondary school mathematics are assumed. |
| Basic initial knowledge and skills of secondary school mathematics are assumed. |
| learning outcomes |
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| Memorize the formulas for the discriminant and the solution of the quadratic equation. |
| Memorize the formulas for the discriminant and the solution of the quadratic equation. |
| Define the values of trigonometric functions on the angles of a right triangle. |
| Define the values of trigonometric functions on the angles of a right triangle. |
| Define the concepts: the polynomial, the root of polynomial and its multiplicity. |
| Define the concepts: the polynomial, the root of polynomial and its multiplicity. |
| Explain the basic concepts of vectors and matrices. |
| Explain the basic concepts of vectors and matrices. |
| Explain the meaning of the coefficients in the linear form of the equation of a line. |
| Explain the meaning of the coefficients in the linear form of the equation of a line. |
| Skills |
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| Take out before the parenthesis, edit and simplify the algebraic expressions. |
| Take out before the parenthesis, edit and simplify the algebraic expressions. |
| Simplify the expressions with the powers. |
| Simplify the expressions with the powers. |
| Solve linear and quadratic equations and inequalities. |
| Solve linear and quadratic equations and inequalities. |
| Simplify the expressions with the exponential and logarithmic terms. |
| Simplify the expressions with the exponential and logarithmic terms. |
| Perform arithmetic operations with vectors and matrices. |
| Perform arithmetic operations with vectors and matrices. |
| Calculate the determinant of a square matrix of the 2nd and 3rd order. |
| Calculate the determinant of a square matrix of the 2nd and 3rd order. |
| Use the Gaussian elimination method to calculate the solution to a system of linear equations. |
| Use the Gaussian elimination method to calculate the solution to a system of linear equations. |
| Sketch the graph of a linear function, for two points construct the prescription of a straight line passing through them, convert between each other the slope form of a straight line, a general equation and a parametric expression. |
| Sketch the graph of a linear function, for two points construct the prescription of a straight line passing through them, convert between each other the slope form of a straight line, a general equation and a parametric expression. |
| teaching methods |
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| Knowledge |
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| Lecturing |
| Individual work of students |
| Practice exercises |
| Individual work of students |
| Lecturing |
| Practice exercises |
| assessment methods |
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| Written examination |
| Written examination |
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Recommended literature
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Ostravský J., Polášek V. Diferenciální a integrální počet funkce jedné proměnné - vybrané statě. Zlín, 2011. ISBN 978-80-7454-124-7.
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Petáková, Jindra. Matematika : příprava k maturitě a k přijímacím zkouškám na vysoké školy. 1. vyd. Praha : Prometheus, 1998. ISBN 8071960993.
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Polášek, V., Sedláček, l. & Kozáková, L. Matematický seminář. Zlín: Nakladatelství UTB., 2018.
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