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Lecturer(s)
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Sedláček Lubomír, Mgr. Ph.D.
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Včelař František, RNDr. CSc.
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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
- Preparation for course credit
- 20 hours per semester
- Preparation for examination
- 40 hours per semester
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| prerequisite |
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| Knowledge |
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| Standard knowledge and skills from secondary schools are supposed. |
| Standard knowledge and skills from secondary schools are supposed. |
| learning outcomes |
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| 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. |
| 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 directive form of the equation of a line |
| explain the meaning of the coefficients in the directive form of the equation of a line |
| memorize the formulas for the discriminant and the solution of a quadratic equation |
| memorize the formulas for the discriminant and the solution of a quadratic equation |
| define the values of goniometric functions on the angles of a right triangle |
| define the values of goniometric 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 is a unit, regular, inverse, dese, dterminant matrix |
| describe what is a unit, regular, inverse, dese, dterminant matrix |
| Skills |
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| quote before brackets, modify and simplify algebraic expressions containing broken expressions |
| quote before brackets, modify and simplify algebraic expressions containing broken 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, construct the prescription of a line passing through two points, translate the directive form of the line, the general equation and the parametric expression between each other |
| sketch the graph of a linear function, construct the prescription of a line passing through two points, translate the directive form of the line, the general equation and the parametric expression between each other |
| solve linear equations and inequalities |
| solve linear equations and inequalities |
| sketch the graph of a quadratic function in basic form and after transformations of the vertex equation |
| sketch the graph of a quadratic function in basic form and after transformations of the vertex equation |
| solve quadratic equations using the discriminant or discriminant method, quadratic inequalities using the zero point method |
| solve quadratic equations using the discriminant or discriminant method, quadratic inequalities using the zero point method |
| 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 graphs of goniometric functions |
| sketch graphs of goniometric functions |
| add, subtract, multiply vectors by a scalar, and multiply vectors by a scalar product |
| add, subtract, multiply vectors by a scalar, and multiply vectors by a scalar product |
| add, subtract and multiply numerical matrices |
| add, subtract and multiply numerical matrices |
| calculate the determinant of a square matrix of 2nd and 3rd order |
| calculate the determinant of a square matrix of 2nd and 3rd order |
| use the Gaussian elimination method to calculate the solution of a system of linear equations |
| use the Gaussian elimination method to calculate the solution of a system of linear equations |
| teaching methods |
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| Knowledge |
|---|
| Lecturing |
| Lecturing |
| Individual work of students |
| Individual work of students |
| Practice exercises |
| Practice exercises |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Methods for working with texts (Textbook, book) |
| Demonstration |
| Demonstration |
| Methods for working with texts (Textbook, book) |
| 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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