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Lecturer(s)
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Pavlišta Martin, Ing. Ph.D.
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Kašparová Jana, Mgr. Ph.D.
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Widenská Eva, Ing. Ph.D.
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Jemelka Jiří, Ing. Ph.D.
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Course content
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The concept of real functions of a real variable. The composite function. The inverse function. Elementary functions. Limit and continuity of a function. Derivative. Geometrical and physical meaning. Applications. Derivatives of elementary functions. The basic formulas for differentiation. Differential of a function. Higher derivatives. Investigation of behavior of a function. Primitive functions, indefinite integral. The basic formulas for integration. Integration by parts. Substitution methods. Integration of rational functions. Definite integral and its applications. Improper integral. Basic differential equations. Matrices, determinants. Systems of linear equations. Vectors. Linear dependence and independence of vectors. Scalar product. Vector product. Complex numbers, operations on complex numbers.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with text (with textbook, with book)
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Learning outcomes
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The aim of this course is to provide students with basics of mathematical tools with respect to their study field.
Students will be provided with basics of differential and integral calculus of one variable and with basic linear algebra both through the acquisition of computing skills and the use of web applications.
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Prerequisites
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Not specified.
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Assessment methods and criteria
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Written examination, Student performance assessment, Systematic monitoring
The exam has two parts, both held in writing in full-time form. The first part contains examples of selected topics from high school mathematics. The second part, which can be completed only after completing the first part of the examination, contains examples to the extent discussed during the semester. In case of switching to online teaching, the conditions of completion of the course may change.
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Recommended literature
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Došlá, Zuzana. Matematika pro chemiky. Brno: Masarykova univerzita, 2010. ISBN 978-80-210-5263-5.
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Janeček F., Jindrová P., Zapletal D. Příklady a úlohy ze středoškolské matematiky k přípravě na přijímací zkoušky na VŠ.. Pardubice, 2005.
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Kašparová J., Widenská E. Sbírka vybraných úloh z Matematiky I. Pardubice, 2018. (Studijní materiály v portálu IS/STAG.).
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Kašparová, Jana. Matematika I. Pardubice: Univerzita Pardubice, 2023. ISBN 978-80-7560-473-6.
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Kolda S. - Černá M. Úvod do lineární algebry a analytické geometrie. Pardubice, 2004.
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Kopáček J. Matematická analýza nejen pro fyziky II..
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Polák j. Přehled středoškolské matematiky. Praha, 1972.
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Prachař, Otakar. Průvodce předmětem matematika I.. Pardubice: Univerzita Padubice, 2010. ISBN 978-80-7395-329-4.
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