Mathematical analysis II.2* 1000-114bAM4*
Fubini's Theorem and change of variables in Lebesgue integral - multidimensional case. Volume of a ball in R^n.
Spaces L^p of integrable functions. Convolution and its properties, polynomial approximation of functions.
Absolutely continuous functions.
Lebesgue-Riemann measure on manifolds embedded in R^n. Measure of spheres in R^n. Mass center and Guldin Theorems.
Differential forms and their integrals over oriented manifolds. Manifolds with boundary. Stokes theorem. Special cases in low dimensions (vector analysis in R^3, Green's Theorem,, Classical Stokes Theorem and Divergence (Gauss-Ostrogradski) Theorem, physical applications).
Additional topics:
-elements of de Rham cohomology
-elements of Fourier transformation
-Saard's theorem and its applications
Main fields of studies for MISMaP
mathematics
Type of course
Prerequisites (description)
Course coordinators
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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