| Course title | Mathematics 2 |
|---|---|
| Course code | KMA/MA2-H |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Bachelor |
| Year of study | not specified |
| Semester | Summer |
| Number of ECTS credits | 7 |
| Language of instruction | Czech |
| Status of course | Compulsory, Optional |
| Form of instruction | Face-to-face |
| Work placements | Course does not contain work placement |
| Recommended optional programme components | None |
| Course availability | The course is available to visiting students |
| Lecturer(s) |
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| Course content |
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A. Linear algebra 1. Arithmetic vectors, linear (in)dependence of vectors. Vector space, dimension and basis of a space. 2. Norm of a vector, inner product of vectors. Matrix, operations with matrixes. Rank of a matrix. Gaussian elimination. 3. System of linear algebraic equations, solutions a system of linear algebraic equations. 4. Inverse matrix, properties, calculation of a inverse matrix. Matrix equations, use inverse matrixes to solution matrix equations. 5. Determinant, properties, calculation of determinant. Use: Cramer's rule, calculation of inverse matrix. 6. Eigenvalues and eigenvectors of a matrix. Quadratic forms, properties, Sylvester's criterion. B. Functions of more variables 7. Euclidean n-space, properties of sets of En. Functions of more variables, domain of definition. 8. Partial derivatives, extremes of functions of more real variables. 9. Constrained and global extremes of functions of two variables. C. Differential and difference equations 10. Differential equations of order 1, basic terms. Separation of variable method. 11. Linear differential equations of order 1, variation of constant method. Homogeneous linear equation of order n with constant coefficients (characteristic equation, fundamental system). 12. Heterogeneous linear differential equations with special right side. 13. Difference equations, solution of linear difference equations with constant coefficients.
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| Learning activities and teaching methods |
Monological explanation (lecture, presentation,briefing)
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| Learning outcomes |
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Basis of the linear algebra. Solving of systems of linear algebraic equations. Inverse matrix and their usage, calculation of determinant. Basis of differential calculus for functions of more variables, especially the investigation of extremes of functions of two variables. Differential equations, basic methods for their solving.
Basic knowledge of higher mathematics. |
| Prerequisites |
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Credit from MA1*H
KMA/MA1-E ----- or ----- KMA/MA1-H |
| Assessment methods and criteria |
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Combined examination
Credit: Regular attendance, passing of two tests, working-out of a semestrial work. Exam: written + oral part |
| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester | |
|---|---|---|---|---|
| Faculty: Faculty of Economics | Study plan (Version): Managerial Informatics (2013) | Category: Economy | 1 | Recommended year of study:1, Recommended semester: Summer |
| Faculty: Faculty of Economics | Study plan (Version): Economics and Management of International Trade (2013) | Category: Economy | 1 | Recommended year of study:1, Recommended semester: Summer |