Lecturer(s)
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Fajkus Martin, RNDr. Ph.D.
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Sedláček Lubomír, 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 - Polynomials (roots, Horner´s scheme, division of polynomials, partial fraction decomposition) Notice: Recommended software Mathematica (www.wolfram.com) 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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Lecturing, Monologic (Exposition, lecture, briefing), Demonstration, 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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- 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 determinant of a matrix |
- calculates the determinant of a matrix |
- calculates the inverse matrix |
- calculates the inverse 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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Monologic (Exposition, lecture, briefing) |
Demonstration |
Practice exercises |
Projection (static, dynamic) |
Demonstration |
Projection (static, dynamic) |
Monologic (Exposition, lecture, briefing) |
Lecturing |
Practice exercises |
Lecturing |
assessment methods |
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Grade (Using a grade system) |
Grade (Using a grade system) |
Written examination |
Written examination |
Recommended literature
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Frank Ayers, Elliot Mendelson. Schaums outline of calculus. New York : McGraw-Hill, 1999. ISBN 0070419736.
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WEIR, Maurice D., Joel. HASS, George B. THOMAS a Ross L. FINNEY. Thomas' calculus Boston: Pearson Addison Wesley, 2008. ISBN 032148987X.. Boston: Pearson Addison Wesley, 2008. ISBN 032148987X.
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