Course: Mathematics I

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Course title Mathematics I
Course code UMKM/PMAT1
Organizational form of instruction Lecture + Lesson
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)
  • Gogola Ján, RNDr. Ph.D.
  • Zahrádka Jaromír, RNDr. Ph.D.
  • Brebera Jan, RNDr.
  • Seibert Jaroslav, doc. RNDr. CSc.
  • Jindrová Pavla, Mgr. Ph.D.
  • Janeček František, Mgr.
  • Seinerová Kateřina, Ing.
  • Brebera David, Mgr.
  • Zapletal David, Mgr. Ph.D.
  • Kubát Josef, RNDr.
  • Zahrádková Jiřina, Mgr.
  • Svoboda Martin, RNDr.
  • Horáková Eva, Mgr.
  • Koudela Libor, Mgr. Ph.D.
  • Slavíček Ondřej, Mgr. Ph.D.
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), Methods of individual activities, Skills training
Learning outcomes
The aim of the course is to acquaint the students with basic mathematical appliance 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 and economic problems.
Prerequisites
It is expected the knowledge of the secondary mathematics to the extent of the grammar school.

Assessment methods and criteria
Written examination, Home assignment evaluation, Didactic test

Assignment - active participation in seminars and elaboration of engaged tasks. Passing written test with evaluation at least 40%. Examination - passing a written test with evaluation at least 50%. The test consists of 4 calculating tasks and 5 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.
  • Janeček,F. a kol. Příklady a úlohy ze středoškolské matematiky.. Pardubice, 2005.
  • 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,O. - Cabrnochová,R. Průvodce předmětem MATEMATIKA ( 2. část). Pardubice, 2004.
  • Prachař,O., Jelínková,J. Minimum z předmětu Matematika I (1.část). 2013.
  • Prachař,O. Minimum z předmětu Matematika I (3.část). 2013.
  • Seibert,J.-Kolda,S. Úvod do studia matematiky na Univerzitě Pardubice.. Pardubice, 2007.
  • 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 Public Economics and Administration (2013) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2014) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2016) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2015) 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 Economics and Operation in Enterprises (2015) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2013) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2014) Economy 1 Winter
Faculty of Economics and Administration Economics and Operation in Enterprises (2016) Economy 1 Winter
Faculty of Economics and Administration Economics and Operation in Enterprises (2013) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2016) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2014) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2015) Economy 1 Winter
Faculty of Economics and Administration Security Management in Enterprises (2016) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2013) Economy 1 Winter
Faculty of Economics and Administration Enterprise Management (2013) Economy 1 Winter
Faculty of Economics and Administration Economics and Operation in Enterprises (2014) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2014) Economy 1 Winter
Faculty of Economics and Administration Public Economics and Administration (2013) 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 (2015) Economy 1 Winter