|
|
|
||
Last update: TAJ413 (19.07.2013)
|
|
||
Last update: TAJ413 (19.07.2013)
Students will learn the basics of functional analysis: normed and Hilbert spaces, norms of operators and their spectra. |
|
||
Last update: TAJ413 (19.07.2013)
R: A. E. Taylor: Introduction to Functional Analysis, 2nd ed. Wiley New York, 1980, ISBN-13: 978-0471846468. |
|
||
Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)
http://www.vscht.cz/mat/Ostatni/MIII9-12k.pdf http://www1.maths.leeds.ac.uk/~kisilv/courses/math3263m.html http://www1.maths.leeds.ac.uk/~kisilv/courses/math3263m.pdf |
|
||
Last update: Dubcová Miroslava RNDr. Ph.D. (18.07.2013)
Lectures and exercise classes. |
|
||
Last update: TAJ413 (19.07.2013)
1. Mathematical formulation of classical mechanics and quantum mechanics. 2. Normed linear spaces. Complete spaces. Banach spaces. 3. Spaces with scalar product. Hilbert spaces. 4. Examples. Spaces C(K), spaces c and l. 5. Summation of series, measure and integral, Lebesgue measure and integral. L-spaces. 6. Orthonormal bases of the Hilbert spaces. Fourier series expansion. Bessel inequality. 7. Linear operators and their norms. Dual spaces. 8. Linear forms on Hilbert spaces. Examples of dual spaces. 9. Hahn-Banach theorem and its corollaries. 10. Canonical embeddings, reflexive spaces and orthogonal projections. 11. Spectra of bounded linear operators. Point spectrum. 12. Compact operators and their spectra. 13. Banach algebras. 14. Spectral theory in Hilbert spaces. |
|
||
Last update: TAJ413 (19.07.2013)
Mathematics I, Mathematics II |
Teaching methods | ||||
Activity | Credits | Hours | ||
Konzultace s vyučujícími | 0.5 | 14 | ||
Účast na přednáškách | 1 | 28 | ||
Příprava na přednášky, semináře, laboratoře, exkurzi nebo praxi | 1 | 28 | ||
Příprava na zkoušku a její absolvování | 1.5 | 42 | ||
Účast na seminářích | 1 | 28 | ||
5 / 5 | 140 / 140 |
Coursework assessment | |
Form | Significance |
Regular attendance | 25 |
Continuous assessment of study performance and course -credit tests | 25 |
Oral examination | 50 |