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Lecturer(s)
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Bittner Václav, Mgr. Ph.D.
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Course content
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Lectures: A) Introduction to differential and integral calculus of function of one real variable 1) Number sets; Mapping 2) Real function of one variable; Basic properties of functions and operation with functions 3) Basic elementary functions 4) Sequences (basic concepts, limit of sequence) 5) Limit and continuity of function. Calculation of limit of function. Properties of continuous function. 6) Derivative I (geometric applications, tangent line to a function, calculation of derivative) 7) Derivative II (derivative of a composite function, differential of function, l'Hospital's rule) 8) Relationship between derivation of a function and its course; Investigation of the course of the function 9) Primitive function and indefinite integral. Basic rules, method per partes, substitution method. 10) Riemann definite integral, Newton-Leibniz's theorem. 11) Applications of definite integral; Indefinite integral B) Introduction to linear algebra 12) Arithmetic n-dimensional vector space (linear dependence of vectors, basis and dimension of vector space); Matrix (operations with matrixes, rank and determinant of a matrix) 13) System of linear algebraic equations; Inverse matrix 14) Eigenvalues and eigenvectors of a matrix Exercises: The knowledge from the lecture is practiced. Examples of applications of knowledge in the fields of Biomedical Engineering and Radiology are included. Available software applications are used.
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Learning activities and teaching methods
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Monological explanation (lecture, presentation,briefing)
- Contacts hours
- 70 hours per semester
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Learning outcomes
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The subject represents an introduction to calculus (differential and integral) of function of one real variable and to linear algebra.
A student masters calculus (differential and integral) of function of one real variable and introduction to linear algebra. He is able to use the theory for solving practical problems (extrema of functions, properties of continuous functions on the interval, applications of the proper integral, systems of linear equations, matrix calculus).
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Prerequisites
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Secondary school mathematics.
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Assessment methods and criteria
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Combined examination
Credit: succesful pass of two credit tests, active participation on seminars. Exam: combined exam, it consists of the written theoretical part and practical computations. The results of the tests will be taken into account in the exam.
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Recommended literature
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Bittnerová, D. - Plačková, G. Louskáček 1 - diferenciální počet funkcí jedné reálné proměnné (Sbírka úloh). [Skripta TU v Liberci.] Liberec 2005.. Liberec, 2007.
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Bittnerová, D. - Plačková, G.:. Louskáček 2 - integrální počet funkce jedné proměnné.. TUL, liberec, 2008.
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Černý, M. Výpočty. Tři svazky. Professional Publishing, Praha, 2012.
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DELVENTHAL, K., KISSNER, A., KULICK, M. Kompendium matematiky: vzorce a pravidla, četné příklady včetně řešení: od základních operací po vyšší matematiku.. Praha: Knižní klub, 2013. ISBN 978-80-242-3946-0.
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DOŠLÁ, Zuzana a Petr LIŠKA. Matematika pro nematematické obory: s aplikacemi v přírodních a technických vědách. Praha: Grada, 2014. ISBN 978-80-247-5322-5.
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KAŇKA, Miloš. Matematické praktikum: sbírka řešených příkladů z matematiky pro studenty vysokých škol. Praha: Ekopress, 2010. ISBN 978-80-86929-65-1.
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KAŇKA, Miloš. Sbírka řešených příkladů z matematiky: pro studenty vysokých škol. Praha: Ekopress, 2009. ISBN 978-80-86929-53-8.
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MOC, O.:. Sbírka úloh z matematiky: integrální počet funkcí jedné proměnné.. Ústí nad Labem: UJEP, 2009. ISBN 978-80-7414-183-6.
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