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
Term 2023L: | Term 2024L: |
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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