Mathematical analysis II.1 1000-113bAM3b
Linear and topological structure of Euclidean spaces; transformations, continuity. Calculus in several variables: directional derivative, differentiability, higher-order derivatives, symmetry od the second and higher order differentials, Taylor's formula, the implicit function theorem, local extrema. Manifolds in R^n, tangent spaces, local parametrizations and maps, manifolds defined by a system of equations, normal vectors. Constrained maxima and minima, Lagrange multipliers with
examples.The concept of measure; outer measure and Caratheodory's theorem. Lebesgue measure; measurable functions, Lebesgue integral. Lebesgue monotone
convergence theorem, Lebesgue bounded convergence theorem, the Fatou lemma. Fubini's theorem, change of variables under the integral.
Main fields of studies for MISMaP
mathematics
Type of course
Bibliography
M.Spivak, Modern Approach to Classical Theorems of Advanced Calculus
W.A. Benjamin, L.Bers, Calculus
W.Rudin, Principles of Mathematical Analysis, McGraw-Hill Science Engineering
W.Rudin, Real and Complex Analysis, McGraw-Hill, New York, 1966. xi+412 pp.
Additional information
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