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