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Lecturer(s)
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Sedláček Lubomír, Mgr. Ph.D.
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Fiľo Jaroslav, Mgr.
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Včelař František, RNDr. CSc.
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Hýl Pavel, Mgr.
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Müllerová Zuzana, Mgr. MSc.
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Volaříková Jana, Mgr. Ph.D.
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Course content
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- Vectors, linear combination, linear (in)dependence, vector space - Matrix and matrix operations, rank of a matrix - Determinant, matrix inverse, matrix equations - Systems of linear equations - Functions and their properties - Elementary functions - Limit, continuous function - Derivative - Higher order derivatives, l´Hospital´s rule - Geometric interpretation of first and second derivative - Behavior of a function, graphing
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Projection (static, dynamic), Practice exercises
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| prerequisite |
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| Knowledge |
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| Standard knowledge and computational skills of high school mathematics in a level which allows direct consecution to linear algebra and differential calculus of one variable function. |
| Standard knowledge and computational skills of high school mathematics in a level which allows direct consecution to linear algebra and differential calculus of one variable function. |
| learning outcomes |
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| explain when a set of vectors is linearly dependent/independent |
| The student has knowledge about vectors and matrices and is able to perform basic vector and matrix operations. The student can calculate the determinant of a matrix and the matrix inverse. The student is able to solve systems of linear equations and matrix equations. The student is also well informed in the differential calculus of one variable function issue. The student can calculate limits and derivatives and is able to examine the behavior of a function and draw its graph. |
| explain when a set of vectors is linearly dependent/independent |
| The student has knowledge about vectors and matrices and is able to perform basic vector and matrix operations. The student can calculate the determinant of a matrix and the matrix inverse. The student is able to solve systems of linear equations and matrix equations. The student is also well informed in the differential calculus of one variable function issue. The student can calculate limits and derivatives and is able to examine the behavior of a function and draw its graph. |
| describe what is a unit, regular, inverse, determinant matrix |
| describe what is a unit, regular, inverse, determinant matrix |
| define the concept of a function (a real function of one real variable) and the related concepts of definition domain and value domain |
| define the concept of a function (a real function of one real variable) and the related concepts of definition domain and value domain |
| identify the basic elementary functions based on the graph |
| identify the basic elementary functions based on the graph |
| explain the geometric meaning of the derivative of a function at a point |
| explain the geometric meaning of the derivative of a function at a point |
| Skills |
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| 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, multiply numerical matrices |
| add, subtract, 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 |
| determine and write the defining domain of a function |
| determine and write the defining domain of a function |
| sketch graphs of basic elementary functions and describe their properties |
| sketch graphs of basic elementary functions and describe their properties |
| calculate limits using algebraic adjustments and L'Hospital's rule |
| calculate limits using algebraic adjustments and L'Hospital's rule |
| derive elementary, composite, product and quotient functi |
| derive elementary, composite, product and quotient functi |
| determine the stationary points of the function and decide on the type of possible extreme |
| determine the stationary points of the function and decide on the type of possible extreme |
| find the inflection points of the function and the intervals on which the function is convex/concave |
| find the inflection points of the function and the intervals on which the function is convex/concave |
| teaching methods |
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| Knowledge |
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| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| Practice exercises |
| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Practice exercises |
| assessment methods |
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| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Written examination |
| Written examination |
| Oral examination |
| Oral examination |
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Recommended literature
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Kaňka M., Henzler J. Matematika 2. Ekopress Praha, 2003. ISBN 80-86119-77-7.
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Klůfa J., Coufal J. Matematika 1. Ekopress Praha, 2003. ISBN 80-86119-76-9.
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Olšák P. Úvod do algebry, zejména lineární. FEL ČVUT Praha, 2007.
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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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