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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 the differential and integral calculus of functions of one real variable 1) Numerical sets; display 2) Functions of one real variable; basic properties of functions and operations with functions 3) Elementary function 4) Sequences (basic concepts, sequence limit) 5) Limit and continuity of a function; calculation of function limits; properties of continuous functions 6) Derivation of function I (geometric meaning, tangent equation, calculation of derivatives) 7) Derivation of a function II (derivative of a complex function, differential of a function, l'Hospital's rule) 8) The connection between the derivative of a function and its course; investigation of the progress of the function 9) Primitive functions and indefinite integral (basic rules, per partes method, substitution method) 10) Riemann's integral and its calculation 11) Application of a definite integral; It does not have an integral B) Introduction to linear algebra 12) Arithmetic n-dimensional vector space (linear dependence of vectors, basis and dimension of vector space); Nut (matrix operations, rank and determinant of a matrix) 13) Systems of linear algebraic equations; Inverse matrix 14) Eigennumbers and eigenvectors of a matrix Exercises: Knowledge from the lecture is practiced. Examples of applications of knowledge in the fields of Biomedical Technology are included and Radiology. Available sw applications are used.
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Learning activities and teaching methods
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Lecture, Practicum, Students' self-study
- Contacts hours
- 70 hours per semester
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Learning outcomes
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The subject is an introduction to the differential and integral calculus of functions of one real variable and to linear algebra.
Basic knowledge of differential and integral calculus of functions of one real variable and linear algebra.
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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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Written exam, Systematické pozorování studenta, Test
Credit: - awarded for active participation in exercises and for successful completion of prescribed tests and tasks. Exam: - written, consists of a numerical and theoretical part, - the assessment from the exercise will be taken into account when grading the exam.
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Recommended literature
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BEČVÁŘ, J.:. Lineární algebra. Praha : Matfyzpress, 2019. ISBN 978-80-7378-378-5.
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DOŠLÝ, O., ZEMÁNEK, P. Integrální počet v R. Brno: Masarykova univerzita, 2011. ISBN 978-80-210-5635-0.
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Klůfa, J. Základy matematiky pro Vysokou školu ekonomickou. Ekopress, Praha, 2021. ISBN 978-808-7865-729.
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MUSILOVÁ, J., MUSILOVÁ, P. Matematika pro porozumění i praxi: netradiční výklad tradičních témat vysokoškolské matematiky. Brno: VUTIUM, 2017. ISBN 978-80-214-5503-0.
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PETÁKOVÁ, J. Matematika - příprava k maturitě a k přijímacím zkouškám na vysoké školy. Praha, 2020. ISBN 978-80-7196-487-2.
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POLÁK, J. Přehled středoškolské matematiky. Praha, Prometheus, 2015. ISBN 978-807-1964-582.
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