1. Normed spaces (normed speces, topology of a normed space, equivalent norms, equivalence of all the norms in finitedimensional spaces, the natural topology of a finitedimensional space, basic normes, product of normed spaces, compact sets in a finitedimensional space, continuity of some basic mappings). 2. The first derivative (Fréche derivative, Gateaux derivative, directional derivative, differential, their basic properties and relations between them, derivatives of basic mappings, Chain Rule and its corollaries, partial derivatives, continuous differentiability). 3. Theorems on inverse function and on imlicite function (Banach spaces, contraction lemma, Theorem on inverse function, Theorem on imlicite function). 4. Higher derivatives (definition and properties of higher derivatives, symmetry of higher derivatives, higher partial derivatives, Taylor formula, extreme problems without constrains, Fermat theorem, necessary conditions and sufficient conditions of the second order for local extremum, extreme problems with constrains, tangent vectors and normal vectors, necessary condition of local extremum in problems with constrains in terms of normal vectors, Lagrange Theorem on multiplicators).


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