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Lecturer(s)
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Knobloch Roman, RNDr. Ph.D.
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Bittner Václav, Mgr. Ph.D.
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Course content
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A. Differential calculus 1. Number sets. mapping, basic terms (domain of definition, image of mapping, types of mapping). 2. Real function of one variable. Basic elementary functions. Basic properties of functions and operation with functions. 3. Limit and continuity of functions. Calculation of limits. Properties of continuous function. 4. Derivative, geometric applications, tangent line to a function. Calculation of derivative, derivative of a composite function. 5. Convexity, concavity, point of inflexion, applications of derivative to studying of graph of a function (monotony, local and global extreme, convexity, concavity, point f inflexion). Asymptote. B. Integral calculus 6. Primitive function and indefinite integral. Basic rules, method per partes, substitution method. 7. Riemann definite integral, Newton-Leibniz's theorem. 8. Applications of definite integral. 9. Number series, criterions of convergence, absolute convergence. C. Linear algebra 10. Arithmetics vectors, linear (in)dependence of vectors. Vector space, dimension and basis of space. 11. Matrix, operations with matrixes. Rank of a matrix. Determinant, properties, calculation of determinant. 12. System of linear algebraic equations, solution of a system of linear algebraic equations. Gaussian elimination method. Cramer's rule. 13. Inverse matrix, properties, calculation of determination. 14. Matrix equations, use inverse matrixes to solution matrix equations.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Class attendance
- 56 hours per semester
- Semestral paper
- 15 hours per semester
- Preparation for credit
- 30 hours per semester
- Home preparation for classes
- 60 hours per semester
- Preparation for exam
- 50 hours per semester
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Learning outcomes
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In this course, students will learn the mathematical terms and procedures that they will use during their studies in radiology. In particular, they will use mathematical knowledge to description of physical fields. Students will study the basics of differential and integral calculus, series and the basics of linear algebra.
Basic knowledge of higher mathematics.
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Prerequisites
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Knowledge of mathematics at the high school level
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Assessment methods and criteria
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Combined examination
Credit: knowledge of mathematics at the high school level, regular attendance, passing of three tests
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Recommended literature
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Bittnerová, D. - Plačková, G.:. Louskáček 1 - Diferenciální počet funkcí jedné reálné proměnné (Sbírka úloh). Liberec, TUL 2006, 2007..
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Bittnerová, D. - Plačková, G.:. Louskáček 2 - Integrální počet funkcí jedné reálné proměnné..
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Kaňka, M. - Henzler J.:. Matematika 2, Ekopress.. Praha, 2003. ISBN 80-86119-77-7.
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Klůfa, J. - Coufal, J.:. Matematika 1, Ekopress.. Praha, 2003. ISBN 80-86119-76-9.
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Vild, J. - Říhová, H.:. Diferenciální kalkul F1.. Liberec, 2002. ISBN 80-7083-552-4.
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Vild, J. - Říhová, H.:. Integrální kalkul F1.. Liberec, 2005. ISBN 80-7083-587-7.
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