Předmět Mathematical Logic and Graph Theory - INFOA (EAE55E)

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Materiál	Typ	Datum	Počet stažení

Osnova

PřednáškaEquations, inequalities, radicals, binomial expressions, polynomials, fractions, complex numbersFunctions, algebraic functions, transformation, inverse, plottingNon-algebraic functions, transformation, inverse, plottingAnalytic geometry in V2, lines, conic sectionsLimits and continuity 1: Definition, one/two-sides limits, calculating using limit laws, direct substitution propertyLimits and continuity 2: Indefinite limits, indeterminate forms of limits, vertical/oblique asymptotesLimits and continuity 3: Special limits, continuity of functionDerivatives 1: Tangent/normal lines, slopes, position and velocity, acceleration, definition of derivativeDerivatives 2: Differentiation rules for algebraic and non-algebraic functions, chain ruleDifferentiability and continuity, implicit derivation, l´Hospital ruleApplication of the Derivative 1: Maximum and minimum values, local and global maxima and minimaTheory of graphsCvičeníHigher algebraic operationsTransformation of algebraic functions, inverse function, plottingTransformation of non-algebraic functions, inverse function, plottingLines, conic sectionsLimits, limit laws, limits and continuity of the functionDomain of the functionSlope of the functionDifferentiation of functionsDifferentiation of functionsDerivatives of implicit functionsMaximum and minimum values, local and global maxima and minimaGraphs

Získané způsobilosti

Znalosti:Undergraduates fructified successfully mathematical grounding of secondary education level to apply and develop it to higher level of advanced calculus at bachelor level of study. Students understand relation from small-scale (differential) quantities to large-scale (integrated) quantities. They understand basic mathematical concepts, terms and procedures used by exact used of theorems and proves, know the essence of the function, limit of the function and process of differentiation. They see mathematics as a necessary tool for solutions of various technical and societal problems and a base of their future undergraduate study.Dovednosti:Undergraduates can apply theoretical and practical knowledge of the differentiation of the functions in creating solutions to other similar single well-defined mathematical problems. They passed topics differentiation of functions of one variable, with applications, informal treatment of limits and continuity, differentiation (definition, rules, application to graphing, rates, approximations, and extreme problems). Students should demonstrate an understanding the derivative as a rate of change, and of the inverse relationship between integration and differentiation. They have skills to analyse, identify properties and plot the graphs of simpler composed algebraic and transcendental functions.Kompetence - komunikace:Graduates are capable of communication with other professionals using basic calculus in the practice. They know basic mathematical vocabulary, use it in English communication. Produce detailed written and oral communication in situations in which play some role basic calculus. They convey ideas in a well structured and coherent way to peers, supervisors and clients using quantitative information at bachelor calculus level.Kompetence - úsudek:Undergraduates are able to evaluate and critically assess their study and plan other quantitative courses. The obtained level of calculus makes them possible to present and justify mathematical approaches to solution of a problem before public. They can judge if the given problem is easy to solve independently or ask for assistance. They also are able to measure the reliability of their decision making supported by calculus.

Literatura

ZákladníStewart, James (2009) Calculus.Metric International Version Calculus, 6ed., Brooks/Cole. ISBN 13 978-0-495-38362-8.DoporučenáStewart, James (2012) Single Variable Calculus.7ed., International Edition, Brooks/Cole, ISBN 13 978-0-538-49885-2.Hoffmann, L. D., Bradley, G. L. Finite Mathematics with Calculus, McGraw-Hill, 1995, ISBN 0-07-029325-X.Eric W. Weisstein MathWorld - A Wolfram Web Resource, http//mathworld.wolfram.com.http//en.wikipedia.org/wiki/PortalMathematics.

Požadavky

Basic course of mathematics taught on secondary and higher secondary schools.

Garant

prof. RNDr. Jaroslav Havlíček, CSc.