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Lecturer(s)
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Hrabec Dušan, Ing. Ph.D.
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Krňávek Jan, Mgr. Ph.D.
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Včelař František, RNDr. CSc.
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Volaříková Jana, Mgr. Ph.D.
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Course content
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1. Introduction to expressions and predicate logic. Expression, operations on expressions, formulas, tautology, quantificators. 2. Basic set notions. Set relations, operations on sets, number sets, intervals. Cartesian product, relations, maps. 3. Elementary functions and their properties. Linear function, quadratic, power, exponential, logarithmic, goniometric and cyclometric functions. 4. Polynomials and their properties. Methods of searching for the zeros. Horner's schema. 5. Expressions, equations, inequalities. Modifications and rearrangements of algebraic expressions. Solving of linear, quadratic, exponential, logarithmic, goniometric and cyclometric equations and inequalities. 6. Sequences and series. Arithmetic and geometric sequence. Geometric series. 7. Analytical geometry. Line in the plane and in the space. Equation of a plane. Conic sections. 8. Vectors, operations with vectors. Linear dependence and independence of vectors. Vector space. Scalar and vector product of vectors. 9. Matrices, basic notions and properties. Operations with matrices. Rank of matrices. 10. Determinant of a matrix. Inverse matrix calculation. 11. Solving of a system of linear equations using Gauss elimination method. Cramer's rule. 12. Complex numbers. Forms of complex numbers. Moivre theorem.
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Learning activities and teaching methods
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Lecturing, Methods for working with texts (Textbook, book), Demonstration, Projection (static, dynamic), Practice exercises, Individual work of students
- Home preparation for classes
- 28 hours per semester
- Participation in classes
- 84 hours per semester
- Preparation for course credit
- 20 hours per semester
- Preparation for examination
- 30 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| Standard knowledge and skills from secondary schools are supposed. |
| Standard knowledge and skills from secondary schools are supposed. |
| learning outcomes |
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| Explain the meaning of the coefficients in the linear form of the equation of a line. |
| Students will complete the basic high school knowledge and skills needed for further study of mathematical analysis. They are also able to solve standard problems of linear algebra, matrix calculus, analytical geometry in space and is able to analyze, model and solve interdisciplinary problems by methods of linear algebra. |
| Explain the meaning of the coefficients in the linear form of the equation of a line. |
| Students will complete the basic high school knowledge and skills needed for further study of mathematical analysis. They are also able to solve standard problems of linear algebra, matrix calculus, analytical geometry in space and is able to analyze, model and solve interdisciplinary problems by methods of linear algebra. |
| 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. |
| Explain when a set of vectors is linearly dependent/independent. |
| Explain when a set of vectors is linearly dependent/independent. |
| Describe what a unit, regular, inverse matrix is. |
| Describe what a unit, regular, inverse matrix is. |
| Skills |
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| Take out before the parenthesis, edit and simplify the algebraic expressions containing the expressions. |
| Take out before the parenthesis, edit and simplify the algebraic expressions containing the expressions. |
| Modify and simplify expressions with powers and square roots. |
| Modify and simplify expressions with powers and square roots. |
| 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. |
| Solve linear equations and inequalities. |
| Solve linear equations and inequalities. |
| Sketch the graph of the quadratic function in the basic form and after transformations of the vertex equation. |
| Sketch the graph of the quadratic function in the basic form and after transformations of the vertex equation. |
| Solve quadratic equations by taking out or through the discriminant, quadratic inequalities by the method of zero points. |
| Solve quadratic equations by taking out or through the discriminant, quadratic inequalities by the method of zero points. |
| Sketch the graphs of exponential and logarithmic functions. |
| Sketch the graphs of exponential and logarithmic functions. |
| Use basic adjustments when working with exponentials and logarithms. |
| Use basic adjustments when working with exponentials and logarithms. |
| Sketch the graphs of trigonometric functions. |
| Sketch the graphs of trigonometric functions. |
| Add vectors, subtract them, multiply them by a scalar and multiply each other by a scalar product. |
| Add vectors, subtract them, multiply them by a scalar and multiply each other by a scalar product. |
| Add, subtract and multiply number matrices. |
| Add, subtract and multiply number 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. |
| teaching methods |
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| Knowledge |
|---|
| Lecturing |
| Lecturing |
| Individual work of students |
| Individual work of students |
| Demonstration |
| Demonstration |
| Methods for working with texts (Textbook, book) |
| Methods for working with texts (Textbook, book) |
| Practice exercises |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Practice exercises |
| assessment methods |
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| Written examination |
| Written examination |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
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Recommended literature
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BARNETT, Raymond A. Intermediate algebra. 4 ed.. New York: McGraw-Hill Book Company, 1990. ISBN 0070039461.
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Doležalová, Jarmila. Mathematics I.. Ostrava: VŠB - Technical University of Ostrava, 2005. ISBN 8024807963.
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GILBERT, William J a W. Keith NICHOLSON. Modern algebra with applications.. 2004. ISBN 0471414514.
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LIAL, Margaret L., John P. HOLCOMB a Thomas W. HUNGERFORD. Finite mathematics with applications in the management, natural and social sciences. Boston: Pearson/Addison-Wesley, 2007. ISBN 0321386728.
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Matejdes, Milan. Aplikovaná matematika. Zvolen, 2005. ISBN 80-89077-01-3.
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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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Polák, Josef. Přehled středoškolské matematiky. 8. vyd. Praha : Prometheus, 2003. ISBN 8071962678.
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TURZÍK, Daniel, Miroslava DUBCOVÁ a Pavla PAVLÍKOVÁ. Základy matematiky pro bakaláře.. Praha, 2011. ISBN 978-80-7080-787-3.
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