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Lecturer(s)
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Dofková Radka, doc. PhDr. Ph.D.
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Laitochová Jitka, doc. RNDr. CSc.
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Course content
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unspecified
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Differential calculus of functions of two or more variables. Applications of partial derivatives are demonstrated. Main topics: n-dimensional space, metric space, Euclidean space. Neighbourhood of n-dimensional space. Function of several variables. Domain and range. Geometric meaning of the function z = f (x, y). Limit of a function of several variables. Improper limit. Continuity of functions of several variables. Composite functions of several variables. Theorem on the continuity of composite functions. Partial derivatives of functions of several variables. Geometrical meaning of partial derivative of a function f (x, y). Higher partial derivatives. Schwarz theorem. Differentiable function. Complete differential. Geometrical meaning of the complete differential df(x, y). Complete differentials of higher orders. Partial derivatives of composite functions. Higher derivatives of a composite function. Taylor and Maclaurin's formula. Maxima, Minima, and Saddle Points. Fermat's theorem Sufficient conditions for local extrema. Implicit functions and their derivatives. Theorems on the existence of a derivative of an implicit function expressed by the equation F (x, y) = 0 and the equation F (x, y, z) = 0
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Prerequisites
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unspecified
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Assessment methods and criteria
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unspecified
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Recommended literature
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LARSTON, R., HOSTETLER, R., EDWARDS B.H. (2008). Precalculus.Functions and Graphs. A graphic approach..
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Spivak, M. (1994). Calculus. Cambridge: Cambridge University Press, 670 s.
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THOMAS, G.B., FINNEY, R.L. (1989). Calculus and analytic geometry. Addison-Wesley Publishing Company.
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