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Lecturer(s)
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Teska Jakub, RNDr. Mgr. Ph.D.
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Skyvová Mária, Mgr.
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Holub Přemysl, Doc. RNDr. Ph.D.
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Šebková Milena, RNDr.
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Ekstein Jan, RNDr. Ph.D.
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Course content
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1st week - Complex numbers - definition, Gaussian plane, calculus, trigonometric and exponential form of a complex number, solving quadratic equations in complex domain 2nd-3rd week - Polynomials - calculus, roots of a polynomial, Horner scheme, factorization of a polynomial, decomposition of a rational function into partial fractions 4th week - Martix - basic definitions, calculus, rank of a matrix 5th-6th week - System of linear algebraic equations - matrix representation, existence of a solution, Gaussian elimination algorithm, inverse matrix 7th-8th week - Linear vector space - linear independence of elements of LVS, basis and dimension of LVS, coordinates of an element of LVS in a given basis 9th week - Determinant of a matrix - calculation, usage for solving a system of linear algebraic equations 10th-11th week - Eigenvalues and eigenvectors of a matrix, Jordan canonical form of a matrix, similarity of matrices 12th-13th week - Inner product - orthogonal projection, least square method
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Learning activities and teaching methods
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- Contact hours
- 39 hours per semester
- Preparation for comprehensive test (10-40)
- 39 hours per semester
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| prerequisite |
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| Knowledge |
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| A knowledge of mathematics and its application taught at ordinary secondary schools are expected |
| Skills |
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| work with terms commonly taught at ordinary secondary schools |
| strandard simplification of algebraic expressions, solving of linear and quadratic equations |
| Competences |
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| N/A |
| learning outcomes |
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| Knowledge |
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| define basic terms from the following fields: Polynomials, Matrices, Linear vector space |
| Skills |
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| among others to solve the following problems: factorization of a polynomial, decomposition of a rational function into partial fractions; system of linear algebraic equations, rank and determinant of a matrix, inverse matrix, eigenvalues and eigenvectors of a matrix; the Least square method |
| teaching methods |
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| Knowledge |
|---|
| Interactive lecture |
| Practicum |
| Skills |
|---|
| Interactive lecture |
| Practicum |
| Competences |
|---|
| Interactive lecture |
| Practicum |
| assessment methods |
|---|
| Knowledge |
|---|
| Test |
| Continuous assessment |
| Skills |
|---|
| Test |
| Continuous assessment |
| Competences |
|---|
| Test |
| Continuous assessment |
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Recommended literature
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Lütkepohl, Helmut. Handbook of matrices. Chichester : Wiley, 1996. ISBN 0-471-97015-8.
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Tesková, Libuše. Lineární algebra. 3. vyd. Plzeň : Západočeská univerzita, 2010. ISBN 978-80-7043-966-1.
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Tesková, Libuše. Sbírka příkladů z lineární algebry. 5. vyd. Plzeň : Západočeská univerzita, 2003. ISBN 80-7043-263-2.
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Watkins, David S. Fundamentals of matrix computations. 2nd ed. New York : John Wiley & Sons, 2002. ISBN 0-471-21394-2.
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