Course: Mathematics I

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Course title Mathematics I
Course code UMKM/PMT1
Organizational form of instruction Lecture + Lesson
Level of course Bachelor
Year of study 1
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)
  • Zapletal David, Mgr. Ph.D.
  • Brebera David, Mgr.
  • Jindrová Pavla, Mgr. Ph.D.
  • Koudela Libor, Mgr. Ph.D.
  • Brebera Jan, RNDr.
  • Seinerová Kateřina, Ing.
  • Svoboda Martin, RNDr.
  • Papoušková Monika, Ing.
  • Gogola Ján, RNDr. Ph.D.
  • Seibert Jaroslav, doc. RNDr. CSc.
Course content
Mathematical logic - statements, logical connectives, quantifiers. Set theory - operations with sets, sets of numbers, relations and mappings. Sequences of real numbers and their limits. Functions of a real variable - properties, elementary functions, limits and continuity. Differential calculus of functions of a single variable - derivative, differential, theorems on derivatives. Investigation of a function - local extrema, intervals of monotonicity, inflections, concavity, asymptotes. Antiderivatives - elementary methods of calculation. The Riemann and Newton integral, improper integrals, applications. Infinite series - sum, convergence tests, absolute convergence.

Learning activities and teaching methods
Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
Learning outcomes
The course is designed to acquaint students with basics of analysis, differential and integral calculus of functions of one real variable and theory of infinite series and to develop the logical thinking of students and their ability to find and use appropriate mathematical methods to solve problems of various economic and technical disciplines.
Students will be able to solve problems of all topics covered by this course and to find and use appropriate methods to solve problems of subsequent mathematically oriented subjects.
Prerequisites
Secondary school mathematics.

Assessment methods and criteria
Written examination

Assignment - active attendance at seminars and succesfully answered written test. Examination - a set of theoretical questions and a set of problems.
Recommended literature
  • Cabrnochová,R.-Prachař,O. Průvodce předmětem MATEMATIKA I (první část).. Pardubice, 2004.
  • Cabrnochová,R.-Prachař,O. Průvodce předmětem Matematika I (druhá část).Úlohy z diferenciálního a integrálního počtu funkcí jedné reálné proměnné.. Pardubice, 2007.
  • Janeček,F. a kol. Příklady a úlohy ze středoškolské matematiky.. Pardubice, 2005.
  • Jindrová, Pavla. Sbírka řešených příkladů z matematiky s aplikacemi v ekonomii : distanční opora. Pardubice: Univerzita Pardubice, 2011. ISBN 978-80-7395-428-4.
  • Koudela, L., a kol. Matematika I.. Pardubice: Univerzita Pardubice, 2012. ISBN 978-80-7395-460-4.
  • Machačová, L. Základy diferenciálního a integrálního počtu. Pardubice, 2007.
  • Prachař,O.-Cabrnochová,R. Průvodce předmětem Matematika I (třetí část). Úlohy z lineární algebry, analytické geometrie a z nekonečných řad.. Pardubice, 2007.
  • Seibert,J.-Kolda,S. Úvod do studia matematiky na Univerzitě Pardubice.. Pardubice, 2007.


Study plans that include the course