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Advanced Differentiation and Integration 2 - NMMA438

Title:	Derivace a integrál pro pokročilé 2
Guaranteed by:	Department of Mathematical Analysis (32-KMA)
Faculty:	Faculty of Mathematics and Physics
Actual:	from 2016 to 2016
Semester:	summer
E-Credits:	4
Hours per week, examination:	summer s.:2/0, Ex [HT]
Capacity:	unlimited
Min. number of students:	unlimited
4EU+:	no
Virtual mobility / capacity:	no
State of the course:	not taught
Language:	Czech, English
Teaching methods:	full-time
Teaching methods:	full-time

Class:	M Mgr. MA M Mgr. MA > Povinně volitelné
Classification:	Mathematics > Real and Complex Analysis

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Annotation -

Last update: T_KMA (02.05.2013)

Sets of finite perimeter, Gauss-Green theorem, pointwise properties of BV functions, Stokes theorem for nonsmooth data, rectifiability, definition of currents. Recommended for master students of mathematical analysis.

Literature

Last update: doc. Mgr. Petr Kaplický, Ph.D. (09.06.2015)

L. Ambrosio, N. Fusco, D. Pallara: Functions of bounded variation and free discontinuity problems. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, New York, 2000.

H. Federer: Geometric measure theory. Classics in Mathematics, Springer 1996.

L.C. Evans, R.F. Gariepy: Measure theory and fine properties of functions. Studies in Advanced Mathematics. CRC Press, Boca Raton, FL, 1992

Syllabus -

Last update: doc. Mgr. Petr Kaplický, Ph.D. (09.06.2015)

1. Rectifiable sets

Rectifiability

Tangent spaces

C-1 approximation

Densities

Differential forms and currents

2. BV functions of several variables

Essential variations on lines

Convergence of BV functions (strong, weak, strict)

Pointwise properties of BV functions

3. Sets of finite perimeter

Federer boundary and its rectifiability

Gauss-Green theorem

Characterization by the essential boundary

4. Lipschitz manifolds

Lipschitz atlas

Orientation

Stokes theorem