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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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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)
- 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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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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Knowledge of mathematics at the high school level
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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). 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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