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Last update: T_KDM (04.05.2012)
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Last update: T_KDM (04.05.2012)
This subject helps to see the whole picture as for the requirements of bachelor's exam. The aim is to complete, to consolidate and to organize key mathematical knowledge and skills, to develop discovering of relations between particular mathematical disciplines. Last but not least, student will be encouraged to creative approach to mathematics. |
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Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (29.10.2019)
Necessary and sufficient condition for obtaining credit is
while
The student has the opportunity to repeat this part.
Active participation in the seminar is strongly recommended. |
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Last update: T_KDM (04.05.2012)
Veselý, J. Matematická analýza pro učitele I. Matfyzpress, 1997. Veselý, J. Matematická analýza pro učitele II. Matfyzpress, 1997. Brabec, J. a kol. Matematická analýza I. SNTL, 1989. Brabec, J., Hrůza, B. Matematická analýza II. SNTL, 1986. Černý, I. Úvod do inteligentního kalkulu. Academia, 2002. Černý, I. Úvod do inteligentního kalkulu 2. Academia, 2005. Bečvář, J. Lineární algebra. Matfyzpress, 2002. Sekanina, M. a kol. Geometrie I. SPN, 1986. Sekanina, M. a kol. Geometrie II. SPN, 1988. Janyška, J., Sekaninová, A. Analytická geometrie kuželoseček a kvadrik. Brno, 1996. Blažek, J. a kol. Algebra a teoretická aritmetika I. SPN, 1983. Blažek, J. a kol. Algebra a teoretická aritmetika II. SPN, 1985. Děmidovič, B. P. Sbírka úloh a cvičení z matematické analýzy. Fragment, 2003.
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Last update: Mgr. Zdeněk Halas, DiS., Ph.D. (29.10.2019)
This is a seminar. |
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Last update: T_KDM (04.05.2012)
Actual topics will be established mainly on the basis of questions of students and on the monitoring of their needs. The set of all possible topics is determined by contents of bachelor exam:
1. Relations, mappings and their basic properties. 2. Construction and properties of number domains. 3. Groups and their homomorphisms. 4. Ring, integral domain, division ring and their basic properties. 5. Vector space, base, dimension, linear mapping. Vector space equipped with dot product, cross product. 6. Matrices and their properties, application for solution of systems of linear equations. 7. Determinants and their properties, Cramer's rule. 8. Basic concepts of divisibility in integral domains. 9. Differential calculus of functions of one real variable - limit, continuity, derivative, Taylor's theorem, behaviour of a function. 10. Elementary functions and their definition. 11. Primitive function. Integration by parts and substitution. 12. Riemann integral and its applications, improper integrals. 13. Sequences of real numbers, limits. 14. Infinite series and their sums. Basic theorems concerning absolute and nonabsolute convergence, criteria of convergence. 15. Differential equations, basic methods of their solution. 16. Affine and Euclidean space. 17. Groups of geometric projections.
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