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Lecturer(s)
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Koudela Libor, Mgr. Ph.D.
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Course content
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Limit of sequence, limits and continuity of functions of one real variable Derivative of a function of one real variable, the introduction and basic properties. Higher order derivatives, the selected applications of the derivative of a function. The investigation of the graph of a function by using the derivatives. Extreme values of functions of one real variable. The indefinite integral, introduction and basic properties. The definite integral, basic properties. The calculation methods of indefinite and definite integrals, simple applications. Vectors and vector spaces. Matrices. Basic operations with matrices. Determinant of a matrix, basic properties and methods of calculation. Inverse matrices, methods of calculation. Solving systems of linear equations. Application of the course material in solving some typical problems of economic practice.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Work with text (with textbook, with book), Methods of individual activities, Skills training
- Contact teaching
- 14 hours per semester
- Preparation for a credit (assessment)
- 25 hours per semester
- Preparation for an exam
- 111 hours per semester
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Learning outcomes
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The aim of the course is to teach the student to use the appropriate mathematical knowledge in specialized courses of study and after leaving for practice.
A student who has successfully completed the course can: characterize the principle of methods used to investigate the properties of functions or the relationships between them; explain the important properties of functional dependencies between the variables under study determined by derivatives of functions; explain the basic concepts of differential and integral calculus of functions of one real variable. A student who has successfully completed the course will be able to: apply logical thinking and numerical proficiency to increase independence in problem solving in mathematical models and situations in various fields of economics; actively apply learned concepts and methods in the formulation and solution of optimization problems leading to the search for extremes of functional relationships with one or two independent variables; recognize differential relationships between variables and find appropriate functional relationships that satisfy them. A student who has successfully completed the course is able to: include in problem solving considerations leading to an assessment of the realism of the results obtained.
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Prerequisites
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It is expected the knowledge of the secondary mathematics to the extent of the grammar school.
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Assessment methods and criteria
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Written examination, Home assignment evaluation, Didactic test
Assignment - active participation in seminars and elaboration of engaged tasks. Examination - passing a written test with evaluation at least 50%. The test consists of theoretical questions problems to be solved.
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Recommended literature
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HOY, Michael. Mathematics for economics. Cambridge: Mass., 2011. ISBN 978-0-262-51622-8.
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JINDROVÁ, Pavla a SEINEROVÁ, Kateřina. Sbírka řešených příkladů z matematiky s aplikacemi v ekonomii: distanční opora. Pardubice, 2011. ISBN 978-80-7395-428-4.
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KAŠPAROVÁ, Jana a PAVLIŠTA, Martin. Matematika I. Pardubice, 2023. ISBN 978-80-7560-473-6.
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KOLDA, Stanislav a ČERNÁ, Milada. Matematika - Úvod do lineární algebry a analytické geometrie. Pardubice, 2007. ISBN 978-80-7395-033-0.
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KOUDELA, Libor a kol. Matematika I: distanční opora. Pardubice. 2017.
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PRACHAŘ, Otakar a JELÍNKOVÁ, Jana. Minimum z předmětu matematika I: distanční opora. Pardubice. 2015.
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