Mathematical analysis II.2 1000-114bAM4b

Change of variables in Lebesgue integral - multidimensional case. Integrals dependent on parameters, their differentiability with respect to parameters. Convolution. Weierstrass Approximation Theorem (e.g. Tonelli polynomials). Curves and surfaces in R^3: curvature and torsion, inner product. Lebesgue-Riemann measure on manifolds embedded in R^n, an example of a polyhedron with small edges and huge area insrcibed in a cylinder. Examples. Mass center and Guldin Theorems. Vector analysis in R^3. Green's Theorem, Classical Stokes Theorem and Divergence (Gauss-Ostrogradski) Theorem with simple physical applications, physical meaning of divergence and rotation. Path integrals independent of the paths. Orientable and nonorientable manifolds in R^n. Remarks on differential forms and general
Stokes Theorem on manifolds with boundary.