Lecturer(s)


Course content

This is the basic course on differential and integral calculus of real functions of one variable. Introduction to mathematical logic and elementary set theory. Sequences of real numbers: limit of a sequence and its basic properties, Euler number e, basic sequence properties  monotone and bounded sequences. Functions of one real variable: definition and basic properties (bounded, monotone, odd, even, periodic, compose, inverse), elementary functions, decomposition of rational functions. Limit and continuity: definitions and basic theorems, evaluation of limits, functions continuous on closed intervals. Weierstrass theorem. Differential Calulus: definition of derivative, motivation from geometry and physics, basic properties, derivatives of elementary functions, differential of function and its applications, higher order derivatives, mean value theorem, l'Hospital rule, Taylor polynomial, Taylor theorem. Course of function: first and second derivatives meaning, local and global extremum, inflection points, vertical and inclined asymptotes, finding a graph of functions. Problems of finding global extrema, derivative of parametrized functions. Primitive functions: definition, basic properties and formulas for elementary functions, perpartes and substitution methods, integration of rational functions, special substitutions. Riemann integral: definition and basic properties, existence, evaluation methods, improper Riemann integral, convergence. Applications of Riemann integral to geometry and physics. Number and function series: definition and basic properties, convergence criteria, power series, Taylor series.

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Projection, Skills training
 unspecified
 78 hours per semester

Learning outcomes

The module is focused to introduce students to the area of elementary mathematical terms, differential and integral calculus function of one's variable and theory of numeral and functional sequences.The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.)
Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.

Prerequisites

Standard mathematical knowns and skills of the mathematics of the middle schools, which make possible to continue the differential and integral onevariable calculus.

Assessment methods and criteria

Written examination
Credit requirements: active participation in seminars with at most three hours absent, and at least 50% success in written test. The course is completed by written exam, at least 55% of success is required. An oral form of the exam is optional, upon a student's request.

Recommended literature


Cabrnochová, Renáta. Průvodce předmětem matematika I.. Pardubice: Univerzita Pardubice, 2004. ISBN 807194694X.

Coufal, J., Klůfa, J. Matematika I pro VŠE. Praha, 1994.

Machačová, L.  Prachař, O.  Kolda, S. Cvičebnice z matematiky I/1. Pardubice, 1997.

Machačová, Ludmila. Matematika : základy diferenciálního a integrálního počtu. Pardubice: Univerzita Pardubice, 2003. ISBN 8071945773.

Prachař, O.  Cabrnochová, R. Průvodce předmětem Matematika (třetí část)  Úlohy z lineární algebry, analytické geometrie a z nekonečných řad.. Pardubice, 2007. ISBN 8071947156.
