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Course, academic year 2019/2020
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Elementary functions - ORMA10103
Title in English: Elementární funkce
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2018
Semester: both
E-Credits: 1
Examination process: combined
Hours per week, examination: 0/0 MC [hours/semester]
Extent per academic year: 8 [hours]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
you can enroll for the course in winter and in summer semester
Guarantor: Mgr. Derek Pilous, Ph.D.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category
Annotation -
Last update: Mgr. Derek Pilous, Ph.D. (08.04.2019)
Basic theory of real functions, elementary functions and methods for solving standard problems connected with them.
Literature - Czech
Last update: Mgr. Derek Pilous, Ph.D. (08.04.2019)

§ Botek, L.: Výukový materiál k základům teorie elementárních funkcí (bakalářská práce). PedF UK, Praha 2016

§ Odvárko, O.: Matematika pro gymnázia - Funkce. 4. vydání. Prométheus, Praha 2008

§ Veselý, J.: Matematická analýza pro učitele I, II. Matfyzpress, Praha 1997

§ Jarník, V.: Diferenciální počet I, II. Academia, Praha 1984

Syllabus -
Last update: Mgr. Derek Pilous, Ph.D. (08.04.2019)

Lectures

Number systems and their properties. Affinely extended real number line R* and its arithmetics. Intervals.

Supremum and infimum for R and R*.

Mapping (general function). Input and output of function, doman and codomain, image and inverse of set. Composition, restriction of function. Inverse fuction, its properties and use.

Function (with codomain in number set). Extrema, supremum and infimum of function. Operations on functions. Injective function.

Boundness in ordered sets and in metric spaces. Case of real numbers.

Monotonic and strictly monotonic functions. Local monotonicity and local extrema. Relation between monotonicity and local monotonicity in Q and in R. Inverse of strictly monotonic function.

Convexity and concavity of function: two definitions, geometric interpretations and equivalence. Inverse of convex and concave function.

Parity and periodicity of function. Properties of even and odd functions, decomposition to even part and odd part. Set of periods, fundamental period. Relation between parity and periodicity of operands and result for arithmetic operations and composition.

Basic real functions: constant, powers, roots, exponential functions, logarithms, trigonometric and inverse trigonometric functions. Properties and formulas. Sign function, indicator function, Dirichlet function.

Elementary functions. Continuity of elementary functions and its consequences. Elementarity of basic functions. Examples of non-elementary functions.

 

Seminar

Solving of inequalities in R, determining domain of elementary functions, linear transformations of graphs of functions, determining inverse of elementary functions.

Course completion requirements - Czech
Last update: Mgr. Derek Pilous, Ph.D. (08.04.2019)

Písemný test (podle sylabu cvičení) a ústní zkouška (podle sylabu přednášek). Ústní zkouška je podmíněna úspěšným absolvováním písemného testu.

 
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