Integrali racionalnih funkcij

Abstract

Keywords

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[N. Hren]
UDC:	512.622.25(043.2)
COBISS:	9797961
Views:	1700
Downloads:	267
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Integrals of rational functions
Secondary abstract:	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.
Secondary keywords:	mathematics;matematika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika-računalništvo
Pages:	29 str.
Type (ePrints):	thesis
Title (ePrints):	Integrals of rational functions
Keywords (ePrints):	razcep racionalne funkcije
Keywords (ePrints, secondary language):	decomposition of rational function
Abstract (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.
Abstract (ePrints, secondary language):	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.
Keywords (ePrints, secondary language):	decomposition of rational function
ID:	8311756