Lecturer(s)


Koudela Libor, Mgr. Ph.D.

Seinerová Kateřina, Ing.

Prachař Otakar, prof. RNDr. CSc.

Seibert Jaroslav, doc. RNDr. CSc.

Course content

Introduction to the propositional and predicate calculus. Sets. Introduction to the mathematical analysis  sequences of real numbers and their limits. Function of one real variable, some special classes of functions, elementary functions. The limit and the continuity of a function. Theorems on the limits of functions. Properties of continuous functions in the closed interval. The differential calculus of a function with one variable  derivative of a function, derivatives of elementary functions. Differentiable functions and the differential of a function. Higher order derivatives. Mean value theorems. Taylor polynominal and its use. Taylor's theorem. L'Hospital's rules. The investigation of the graph of a function by using the differential calculus. The integral calculus of functions with one variable. Primitive functions and the indefinite integral, basic integration methods. The integration of rational functions. The definite integral, the Riemann and the Newton definitions of the definite integral, calculation methods. Some applications of the definite integral. Infinite series  testa for convergence of series of positive numbers, alternating series, absolutely convergent series.

Learning activities and teaching methods

Monologic (reading, lecture, briefing), Work with text (with textbook, with book)

Learning outcomes

The aim of the course is to acquaint the students with basic mathematical knowledge which are necessary in all disciplines of the study specialization in defining and solving concrete problems and for the effective analysis of the onedimensional real system with the continuous or discrete description. Such systems are in the middle of the student's interest along his study as well as during his professional career.
Students will be able to apply obtained skills in solving concrete mathematical, technical and economic problems.

Prerequisites

Knowledge of secondary school mathematics is supposed in the range of grammar school.

Assessment methods and criteria

Written examination, Home assignment evaluation
Assignment  succesfully answered test or submitted solutions of given problems. Examination  written test with evaluation at least 50%. The test consists of calculation tasks and theoretical questions.

Recommended literature


Cabrnochová,R.  Prachař,O. Průvodce předmětem MATEMATIKA I. ( třetí. část ) Úlohy z lineární algebry, analytické geometrie a z nekonečných řad.. Pardubice, 2008.

Cabrnochová,R.  Prachař,O. Průvodce předmětem MATEMATIKA I. (1. část). Pardubice, 2004.

Jindrová,P., Seinerová,K. Zbírka řešených příkladů z matematiky s aplikacemi v ekomii. Univerzita Pardubice, 2011.

Koudela, L. a kol. Matematika I. Univerzita Pardubice, 2012.

Machačová,L. Matematika  Základy diferenciálního a integrálního počtu. Pardubice, 2005. ISBN 8071945573.

Prachař, Otakar. Minimum z předmětu matematika I.. Pardubice: Univerzita Pardubice, 2007. ISBN 9788071949565.

Prachař,O.  Cabrnochová,R. Průvodce předmětem MATEMATIKA ( 2. část). Pardubice, 2004.

Prachař,O. Minimum z předmětu Matematika I (3.část). 2013.

Zahrádka,J., Prachař,O. Minimum z předmětu Matematika I (2.část). 2011.
