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Theory of Integration for Advanced Students I - NMAA075

Title:	Teorie integrálu pro pokročilé I
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2022
Semester:	winter
E-Credits:	3
Hours per week, examination:	winter s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	cancelled
Language:	Czech
Teaching methods:	full-time
Teaching methods:	full-time
Additional information:	http://www.karlin.mff.cuni.cz/~maly

Classification:	Mathematics > Real and Complex Analysis

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Annotation -

Last update: T_KMA (17.05.2004)

Theory of integration in Euclidean spaces, k-dimensional integration in n-dimensional space, integration of differential forms, foundations of geometric measure theory

Literature - Czech

Last update: T_KMA (17.05.2004)

H. Federer: Geometric measure theory, Springer--Verlag, Grundlehren 1969.

J. Lukeš, J. Malý: Míra a integrál, skripta Universita Karlova, Praha 1993.

L. C. Evans, R. E. Gariepy: Measure Theory and Fine Properties of Functions. CRC Press 1992.

L. Simon: Lectures on geometric measure theory, Proc. of the Centre for mathematical analysis, Australian National University, vol.3, 1983.

E.M. Stein: Singular Integrals and Differentiability Properties of Functions, Princeton 1970.

W.P. Ziemer: Weakly Differentiable Functions. Sobolev Spaces and Function of Bounded Variation, Graduate Text in Mathematics 120, Springer-Verlag 1989.

Syllabus -

Last update: T_KMA (17.05.2004)

1. Integration over nonsmooth curves and surfaces, Hausdorff measure, change of variables in integral, area and co-area formula

2. Functions of bounded variation, sets of finite perimeter, divergence theorem

3. Rectifiable sets, differential forms and currents, Stokes theorem and applications