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Lecturer(s)
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Jahodová Berková Andrea, Mgr. Ph.D.
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Brázdová Markéta, Ing. Ph.D.
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Matoušová Ivana, Mgr. Ph.D.
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Kaltounová Vladislava, Ing.
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Kulička Jiří, Mgr. Ph.D.
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Course content
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1. Sequence and its limit (Sequence, limit of sequence, computation of limit of sequences, monotonicity of sequences, convergence and sum of a geometric series) 2. Function and its limit (function, function defined in parts, continuity and limit of function, one-sided limits, rules for calculating limits, calculating type limits of functions) 3. Differential calculus of functions of one real variable (Definition of derivative, theorems on derivatives of powers, goniometric, logarithmic, exponential and cyclometric functions, derivatives of compound functions, differential functions, L'Hospital's rule for calculating limits of functions, tangents and normals) 4. The progression of a function (monotony of a function, stationary points of a function, local and absolute extremes of a function, inflection points of the function, convexity and concavity of the function, asymptotes of the graph of the function, optimization problems) 5. Indefinite integral of functions of one real variable (primitive functions and the indefinite integral, methods of integration - direct, substitution and per partes) 6. The definite integral and its applications (methods of calculating definite integrals, calculating the area under the graph of a function) 7. First order differential equations (initial problem, method of separation of variables, method of variation of a constant, growth models decrease and decrease, logistic model) 8. Differential and integral calculus of functions of two or more real variables (functions of two or more variables, continuity and limit, partial derivatives, geometric meaning of partial derivatives, extremes of functions, Reimann's multivariate integral, calculation of multivariate integrals on a compact interval, application of double integrals)
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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), Methods of individual activities
- Home preparation for classes
- 39 hours per semester
- Contact teaching
- 78 hours per semester
- Preparation for a credit (assessment)
- 25 hours per semester
- Preparation for an exam
- 70 hours per semester
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Learning outcomes
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The objectives of the course are to familiarize students with basic knowledge of sequences and series, functions and their limits, differential and integral calculus, first order differential equations.
Basic knowledge of - sequences and series, functions and their limits, differential and integral calculus, first order differential equations.
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Prerequisites
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General knowledge of basic mathematics from previous studies
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Assessment methods and criteria
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Oral examination, Written examination
Requirements for credit and exam
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Recommended literature
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Jehlička, Vladimír. Matematika I : multimediální studijní opora (videozáznamy přednášek). Pardubice: Univerzita Pardubice, 2014. ISBN 978-80-7395-824-4.
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Jehlička, Vladimír. Matematika 2 : multimediální studijní opora : (videozáznamy přednášek). Pardubice: Univerzita Pardubice, 2013. ISBN 978-80-7395-576-2.
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Jehlička, Vladimír. Matematika 2. Pardubice. 201.
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Jehlička, Vladimír. Sbírka příkladů z Matematiky II. Pardubice: Univerzita Pardubice, 2019. ISBN 978-80-7560-202-2.
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Jehlička, Vladimír. Sbírka příkladů z Matematiky I. Pardubice: Univerzita Pardubice, 2016. ISBN 978-80-7395-967-8.
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Kolda, Stanislav. Cvičebnice z matematiky II. Pardubice: Univerzita Pardubice, 2007. ISBN 978-80-7194-932-9.
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Prachař, Otakar. Průvodce předmětem matematika II.. Pardubice: Univerzita Pardubice, 2003. ISBN 80-7194-557-9.
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Prachař, Otakar. Průvodce předmětem matematika I.. Pardubice: Univerzita Padubice, 2010. ISBN 978-80-7395-329-4.
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