Integrali racionalnih funkcij

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2013
Izvor:	Ljubljana
Tipologija:	2.11 - Diplomsko delo
Organizacija:	UL PEF - Pedagoška fakulteta
Založnik:	[N. Hren]
UDK:	512.622.25(043.2)
COBISS:	9797961
Št. ogledov:	1700
Št. prenosov:	267
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Integrals of rational functions
Sekundarni povzetek:	The intention of this diploma thesis is to present the procedure of partial fractions decomposition of rational functions and its use for integration of real and complex rational functions. Laplace theorem, quoted at the beginning, leads us to use complex numbers in the decomposition of rational functions. We use the theorem to show the reason for the partial fraction decomposition, and to emphasize the difference between the decomposition using either real or complex numbers. This difference is later also seen in the procedure of integration. The first two chapters are devoted to finding partial fraction decompositions and their uniqueness. In the next chapter, we present the integration procedures using either real or complex decomposition, and show that they both give the same result.
Sekundarne ključne besede:	mathematics;matematika;
Vrsta datoteke:	application/pdf
Vrsta dela (COBISS):	Diplomsko delo/naloga
Komentar na gradivo:	Univ. Ljubljana, Pedagoška fak., Matematika-računalništvo
Strani:	29 str.
Vrsta dela (ePrints):	thesis
Naslov (ePrints):	Integrals of rational functions
Ključne besede (ePrints):	razcep racionalne funkcije
Ključne besede (ePrints, sekundarni jezik):	decomposition of rational function
Povzetek (ePrints):	V diplomski nalogi je predstavljen postopek razcepa racionalne funkcije na parcialne ulomke, katerega uporabljamo pri integriranju tako realne kot kompleksne racionalne funkcije. Na začetku diplome je citiran Laplacev izrek, preko katerega pridemo do vpeljave kompleksnih števil v razcep racionalne funkcije. S pomočjo tega izreka predstavimo pomen razcepa racionalne funkcije in poudarimo razliko med razcepom racionalne funkcije v kompleksnem in realnem. Ta razlika se nato odraža tudi na samem postopku integracije. V prvih dveh poglavjih predstavimo razcepa racionalne funkcije v realnem in kompleksnem ter njuno enoličnost. V naslednjem poglavju predstavimo postopek integracije v realnem in kompleksnem in pokažemo, da sta rezultata enaka.
Povzetek (ePrints, sekundarni jezik):	The intention of this diploma thesis is to present the procedure of partial fractions decomposition of rational functions and its use for integration of real and complex rational functions. Laplace theorem, quoted at the beginning, leads us to use complex numbers in the decomposition of rational functions. We use the theorem to show the reason for the partial fraction decomposition, and to emphasize the difference between the decomposition using either real or complex numbers. This difference is later also seen in the procedure of integration. The first two chapters are devoted to finding partial fraction decompositions and their uniqueness. In the next chapter, we present the integration procedures using either real or complex decomposition, and show that they both give the same result.
Ključne besede (ePrints, sekundarni jezik):	decomposition of rational function
ID:	8311756