Course: Mathematics I

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Course title Mathematics I
Course code UMKM/KMAT1
Organizational form of instruction Lecture
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
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 one-dimensional 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 80-7194-557-3.
  • Prachař, Otakar. Minimum z předmětu matematika I.. Pardubice: Univerzita Pardubice, 2007. ISBN 978-80-7194-956-5.
  • 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.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Economics and Administration Regional and Information Management (2015) Economy 1 Winter
Faculty of Economics and Administration Economics and Operation in Enterprises (2016) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2015) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2014) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2015) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2014) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2014) Economy 1 Winter
Faculty of Economics and Administration Regional and Information Management (2013) Economy 1 Winter
Faculty of Economics and Administration Economics and Operation in Enterprises (2014) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2014) Economy 1 Winter
Faculty of Economics and Administration Regional and Information Management (2014) Economy 1 Winter
Faculty of Economics and Administration Information and Security Systems (2014) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2014) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2013) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2013) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2016) Economy 1 Winter
Faculty of Economics and Administration Informatics in Public Administration (2014) Economy 1 Winter
Faculty of Economics and Administration Informatics in Public Administration (2013) Economy 1 Winter
Faculty of Economics and Administration Information and Security Systems (2015) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2015) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2016) Economy 1 Winter
Faculty of Economics and Administration Economics and Operation in Enterprises (2013) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2013) Economy 1 Winter
Faculty of Economics and Administration Informatics in Public Administration (2015) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2015) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2013) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2015) Economy 1 Winter
Faculty of Economics and Administration Information and Security Systems (2013) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2016) Economy 1 Winter