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Lecturer(s)
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Marek Jaroslav, Mgr. Ph.D.
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Pozdílková Alena, Mgr. Ph.D.
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Rulićová Iva, RNDr.
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Zahrádka Jaromír, RNDr. Ph.D.
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Rak Josef, RNDr. Ph.D.
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Course content
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1. Mathematical logic (constant, variable, statement, operations with statements). Boolean algebra. 2. Relation, equivalence and arrangement on a set, representation of sets, basic algebraic structures. 3. Functions, basic elementary functions, polynomial, compound function. Inverse function. Function limit, continuity 3. Sequence. Sequence limit. 4. Functions, basic elementary functions, polynomial, composite function. Inverse function. Limit of a function, continuity. 5. Derivation, geometric and physical interpretation, derivation of elementary functions, L'Hospital's rule 6. Differential, geometric interpretation, application of differential for determining approximate values of functions. 7. Extremes of functions. Investigation of the course of a function of one variable. 8. Primitive functions. 9. Definite integral and its applications. 10. Introduction to functions of multiple variables. Partial derivatives. 11. Differential of functions of multiple variables. Local and global extrema of functions of multiple variables. 12. Integral calculus of functions of multiple variables.
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Methods of individual activities, Demonstration, Skills training
- Contact teaching
- 65 hours per semester
- Home preparation for classes
- 50 hours per semester
- Preparation for a credit (assessment)
- 45 hours per semester
- Preparation for an exam
- 50 hours per semester
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Learning outcomes
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The aim of the course to introduce basic mathematical skills to students. Emphasis is placed especially on understanding the main ideas of mathematical methods and the ability of students to apply the methods.
After completing the course, the student demonstrates knowledge of the differential, integral calculus of functions of one and two variables. Can apply mathematical methods to explain, describe and characterize various situations requiring grasp by mathematical tools.
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Prerequisites
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Standard knowledge and calculus skills in high school mathematics at a level that allows direct continuity of differential and integral calculus of functions of one variable.
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Assessment methods and criteria
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Written examination, Work-related product analysis, Didactic test
At least 80% active participation in exercises and passing the credit test in Moodle. A maximum of 3 absences can be replaced by elaboration of a semester work. Recurring student can choose either a 80% participation and recognition test from last year, or at least 50% attendance and a new credit test. The course is completed by written exam, at least 50% of success is required. Classification E 50 % - 55 %, D 56 % - 62 %, C 63 % - 69 %, B 70 % - 76 %, A more than 77 %. An oral form of the exam is optional, upon a student's request.
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Recommended literature
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AYRES, Frank a MENDELSON, Elliot. Schaum's Outline of calculus. New York: McGraw-Hill, 2009. ISBN 0071160361.
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CABRNOCHOVÁ, Renáta a Otakar PRACHAŘ. Průvodce předmětem matematika. 1. Vyd. 3., upr. Pardubice: Univerzita Pardubice, 2004. ISBN 80-7194-715-6.
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KOLDA, Stanislav a Milada ČERNÁ. Matematika - Úvod do lineární algebry a analytické geometrie. Vyd. 10. Pardubice: Univerzita Pardubice, 2007. ISBN 978-80-7395-033-0.
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MACHAČOVÁ, Ludmila. Matematika: základy diferenciálního a integrálního počtu.. Univerzita Pardubice: Vyd. 6, 2010. ISBN 8073953129.
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MAREK, Jaroslav, Karel PASTOR a Alena POZDÍLKOVÁ. Vysokoškolská matematika: výklad, řešené příklady a cvičení. Vyd. 1.. Pardubice: Univerzita Pardubice, 2021. ISBN 978-80-7560-373-9.
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