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Lecturer(s)
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Marek Jaroslav, Mgr. Ph.D.
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Vozáb Jaroslav, Mgr.
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Rak Josef, RNDr. Ph.D.
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Rulićová Iva, RNDr.
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Course content
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1. Introduction to mathematical logic 2. Elementary set theory 3. Sequences of real numbers, limit of a sequence and its basic properties, Euler number e, basic sequence properties - monotone and bounded sequences 4. Functions of one real variable: definition and basic properties (bounded, monotone, odd, even, periodic, compose, inverse), elementary functions 5. Limit and continuity: definitions and basic theorems, evaluation of limits 6. Derivative, definition of derivative, motivation from geometry and physics, basic properties, derivatives of elementary functions, differential of function and its applications, higher order derivatives, Taylor pololynomial 7. Derivative of parametrized and implicit functions 8. Course of function: first and second derivatives meaning, local and global extremum, inflection points, vertical and inclined asymptotes, finding a graph of functions, Problems of finding global extrema 9. Primitive functions: definition, basic properties and formulas for elementary functions, per-partes and substitution methods 10. Integration of rational functions 11. Special substitution in integration 12. Riemann integral: definition and basic properties, existence, evaluation methods, improper Riemann integral, convergence, Newton integral 13. Applications of Riemann integral to geometry and physics
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Learning activities and teaching methods
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Methods of individual activities, Skills training
- unspecified
- 26 hours per semester
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Learning outcomes
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The module is focused to improve and enlarge mathematical skills from module Mathematic I in the field of elementary mathematic conceptions, linear algebra, analytical geometry and differential and integral calculus function of one's variable. The module should increase logical and mathematical skills of the students. Students will be able to understand mathematical conceptions, definitions and operations from this area. They also will gain mathematical skills in such a level that they will be able to apply these skills to following subjects in a particular field of their future study. (electrical and communication technology, microprocessor technology etc.)
Students will be able to solve independently all problems concerning the topics covered by the course Mathematics I. Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology. Students will be able to solve independently all problems concerning the topics covered by the course Mathematics I. Students active use mathematical equipment, are able of logical thinking and are able active to use mathematicel skills in subjects informatics and electrical technology.
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Prerequisites
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Standard knowledge and computational skills in mathematics at secondary school level, which allows direct connection of differential and integral calculus of one variable. The course has a direct link to the lecture and seminar course IMA1E.
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Assessment methods and criteria
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Work-related product analysis
Credit requirements: success in written test (Learn).
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Recommended literature
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Cabrnochová,R. - Prachař,O. Průvodce předmětem Matematika I (druhá část) - Úlohy z diferenciálního a integrálního počtu. Pardubice, 1999.
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Coufal,J., - Klůfa,J. Matematika I pro VŠE. Praha, 1994.
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Kolda,S.-Černá,M. Matematika - Úvod do lineární algebry a analytické geometrie. Pardubice, 2007.
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Machačová, Ludmila. Matematika : základy diferenciálního a integrálního počtu. Pardubice: Univerzita Pardubice, 2003. ISBN 80-7194-577-3.
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Machačová,L.-Prachař,O.-Kolda,S. Cvičebnice z matematiky I/1. Pardubice, 1997.
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Prachař,O. - Cabrnochová,R. Průvodce předmětem Matematika (třetí část) - Úlohy z lineární algebry,analytické geometrie a z nekonečných řad. Pardubice, 2000.
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Seibert,J. - Kolda,S. Úvod do studia matematiky na univerzitě v Pardubicích, skriptum. Pardubice, 1996.
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