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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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Mathematical logic - statements, logical connectives, quantifiers. Set theory - operations with sets, sets of numbers, relations and mappings. Sequences of real numbers and their limits. Functions of a real variable - properties, elementary functions, limits and continuity. Differential calculus of functions of a single variable - derivative, differential, theorems on derivatives. Investigation of a function - local extrema, intervals of monotonicity, inflections, concavity, asymptotes. Antiderivatives - elementary methods of calculation. The Riemann and Newton integral, improper integrals, applications. Infinite series - sum, convergence tests, absolute convergence. Function series, power series, radius and domain of convergence, Taylor series.
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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 course is designed to acquaint students with basics of analysis, differential and integral calculus of functions of one real variable and theory of infinite series and to develop the logical thinking of students and their ability to find and use appropriate mathematical methods to solve problems of various economic and technical disciplines.
Students will be able to solve problems of all topics covered by this course and to find and use appropriate methods to solve problems of subsequent mathematically oriented subjects.
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Prerequisites
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Secondary school mathematics.
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Assessment methods and criteria
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Written examination
Assignment - active attendance at seminars and succesfully answered written test. Examination - a set of theoretical questions and a set of problems.
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Recommended literature
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Finney, Ross L.; Thomas, George B. Calculus and Analytic Geometry.
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Jordan, Dominic W.; Smith, Peter. Mathematical Techniques.
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Pemberton, Malcolm; Rau, Nicholas. Mathematics for Economists.
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