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Lecturer(s)
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Fajkus Martin, RNDr. Ph.D.
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Včelař František, RNDr. CSc.
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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 - Polynomials (roots, Horner´s scheme, division of polynomials, partial fraction decomposition) Notice: Recommended software Mathematica (www.wolfram.com). This software is used in study materials, lectures and text books (see Ostravský, Polášek). And it is available for TBU students free of charge also as a home license.
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Learning activities and teaching methods
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Monologic (Exposition, lecture, briefing), Projection (static, dynamic)
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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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| - clarifies the terms of vector, linear combination, linear dependence |
| - clarifies the terms of vector, linear combination, linear dependence |
| - explains the concepts of matrix, matrix rank, inverse matrix |
| - explains the concepts of matrix, matrix rank, inverse matrix |
| - defines the terms determinant, system of linear equations, matrix equation |
| - defines the terms determinant, system of linear equations, matrix equation |
| - defines the function of one real variable |
| - defines the function of one real variable |
| - explains and clarifies the possible properties of a function |
| - explains and clarifies the possible properties of a function |
| - explains the concepts of limit of a function and derivative of a function |
| - explains the concepts of limit of a function and derivative of a function |
| - clarifies the geometric meaning of the first and second derivatives |
| - clarifies the geometric meaning of the first and second derivatives |
| Skills |
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| - creates a vector that is a linear combination of given vectors |
| - creates a vector that is a linear combination of given vectors |
| - decides whether a given vector is a linear combination of given vectors |
| - decides whether a given vector is a linear combination of given vectors |
| - finds out whether the given vectors are linearly dependent |
| - finds out whether the given vectors are linearly dependent |
| - determines the rank of a matrix |
| - determines the rank of a matrix |
| - calculates the inverse matrix |
| - calculates the inverse matrix |
| - calculates the determinant of a matrix |
| - calculates the determinant of a matrix |
| - solves a system of linear equations |
| - solves a system of linear equations |
| - solves a matrix equation |
| - solves a matrix equation |
| - determines the domain of a function and draws it |
| - determines the domain of a function and draws it |
| - determines the properties of a function |
| - determines the properties of a function |
| - calculates the limit of a function at the specified point |
| - calculates the limit of a function at the specified point |
| - calculates the first and second derivatives of a function |
| - calculates the first and second derivatives of a function |
| - sketches a graph of a specified function |
| - sketches a graph of a specified function |
| teaching methods |
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| Knowledge |
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| Projection (static, dynamic) |
| Projection (static, dynamic) |
| Monologic (Exposition, lecture, briefing) |
| Monologic (Exposition, lecture, briefing) |
| assessment methods |
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| Oral examination |
| Grade (Using a grade system) |
| Grade (Using a grade system) |
| Written examination |
| Written examination |
| Oral examination |
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Recommended literature
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Klůfa J., Coufal J. Matematika 1. Ekopress Praha, 2003. ISBN 80-86119-76-9.
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Křenek, J., Ostravský, J. Diferenciální a integrální počet funkce jedné proměnné s aplikacemi v ekonomii. Zlín: UTB, 2001.
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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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Sklenaříková J., Volfová L. Cvičení z matematiky pro bakaláře. OATB A VOŠE, Zlín, 2004.
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ZEDNÍK, J. Lineární algebra zaměřená na geometrii a ekonomii. UTB ve Zlíně, 2002. ISBN 80-7318-085-5.
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