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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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Linear spaces, linear mappings, matrices. Systems of linear equations, Gaussian elimination. Determinants, Cramer's rule. Linear spaces with a dot product, euclidean space. Functions of several variables - limits and continuity, partial derivatives, differential. Superposition of functions, functions defined implicitly and their derivatives, local extrema. Ordinary differential equations of the first order, the Cauchy problem, separation of variables. Linear differential equations of the first and second order, variation of parameters, method of unknown coefficients. Riemann's multiple integral, Fubini's theorem. Calculation of double integrals, theorem on substitution, improper integrals, applications.
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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 linear algebra, differential and integral calculus of functions of several real variables and theory of ordinary differential equations and to develop 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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unspecified
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Assessment methods and criteria
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Written examination
Assignment - active attendance at seminars, 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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Lang, Serge. Calculus of Several Variables.
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Pemberton, Malcolm; Rau, Nicholas. Mathematics for Economists.
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