Problémy elementární integrace

• Thesis title in Czech: Problémy elementární integrace
• Thesis title in English: Elementary primitives to elementary functions
• Key words: elementární integrace, Liouvilleova věta pro elementární funkci, Čebyševova věta
• English key words: elementary integration, Liouville's theorem for elementary function, Chebyshev's theorem
• Academic year of topic announcement: 2010/2011
• Thesis type: Bachelor's thesis
• Thesis language: čeština
• Department: Department of Mathematical Analysis (32-KMA)
• Supervisor: doc. RNDr. Mirko Rokyta, CSc.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 04.09.2010
• Date of assignment: 22.10.2010
• Date and time of defence: 22.06.2011 00:00
• Date of electronic submission: 25.05.2011
• Date of submission of printed version: 26.05.2011
• Date of proceeded defence: 22.06.2011
• Opponents: prof. RNDr. Jaroslav Lukeš, DrSc.

Guidelines

Student se seznámí s větami Liouvilleova typu, které popisují třídy elementárních funkcí, majících elementární primitivní funkci, a kompilačním způsobem zpracuje toto téma s použitím literatury.

References

R.H.Risch: The problem of integration in finite terms, Trans. Amer. Math. Soc. 139 (1969), 167-189
M. Rosenlicht: Liouville's theorem on functions with elementary integrals, Pacific J. Math. 24 (1968), 153-161

Preliminary scope of work

Funkce exp(-x^2) a sin(x)/x nemaji elementarni primitivni funkci. Proc? A ktere dalsi elementarni funkce maji tuto vlastnost?

Preliminary scope of work in English

The aim is to study elementary functions not having elementary primitive, as sin(x)/x or exp(-x^2).