Linearne preslikave prostora neskončnokrat odvedljivih realnih funkcij

diplomsko delo

Lidija Žugič Vranešević (Author), Dušan Pagon (Mentor)

Abstract

Diplomsko delo je sestavljeno iz dveh poglavij. V prvem poglavju predstavimo osnovne pojme in njihove definicije. Podrobneje se spomnimo linearne preslikave; matrike, prirejene linearni preslikavi; prehoda na novi bazi in podobnosti matrik. Navedemo definicije, dokaze, izreke in za bolje razumevanje si pomagamo tudi z zgledi. V drugem - osrednjem poglavju si ogledamo primere prostorov neskončnokrat odvedljivih realnih funkcij. V razdelku Trigonometrični polinomi in nekateri trigonometrični integrali se ukvarjamo z integriranjem potenc funkcije cos. V linearni algebri se ta problem prevede na problem zamenjave baz. Potem se lotimo integriranja sodih potenc funkcije cos in tudi pri integriranju sode potence funkcije cos si pomagamo s spremembo baze ter prehodnimi matrikami. Nato se ustavimo še pri integriranju potenc funkcije sin. Sledi integriranje nekaterih drugih transcendentnih funkcij, na primerih pa pokažemo, da lahko z uporabo matrik nadomestimo integriranje po delih. Proti koncu si ogledamo tudi reševanje linearnih diferencialnih enačb s konstantnimi koeficienti, kjer uporabimo v prejšnjih razdelkih predelano snov in problem prevedemo na matrike in matrične enačbe.

Keywords

matematika;trigonometrija;polinomi;integriranje;odvajanje;matrike;funkcije;diferencialne enačbe;diplomska dela;

Data

Language:	Slovenian
Year of publishing:	2011
Source:	Maribor
Typology:	2.11 - Undergraduate Thesis
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
Publisher:	[L. Žugič Vranešević]
UDC:	51(043.2)
COBISS:	18834696
Views:	1965
Downloads:	160
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	LINEAR MAPPINGS OF THE SPACE OF INFINITELY DIFFERENTIABLE REAL FUNCTIONS
Secondary abstract:	The graduation thesis is divided into two chapters. In the first chapter the basic concepts and their definitions are represented. We more specifically remember linear transformations, transformation matrices, change of basis and the similarity of matrices. We use these definitions, proofs, theorems and examples for better understanding. In the second central chapter we examine examples of spaces of infinitely differentiable real functions. Under section Trigonometric polynomials and some trigonometric integrals we are dealing with integrating the powers of function cos. In linear algebra this problem translates to the problem of changing the basis. Then we start to integrate even powers of function cos and we do that also with changing the basis and using transition matrices. Then we stop at the integration of powers of function sin. Then follows integration of some other transcendental functions, on examples we show that with matrices we can replace integration by parts. Towards the end we look at solving linear differential equations with constant coefficients, where we use the topics from the previous sections and translate the problem to matrices and matrix equations.
Secondary keywords:	trigonometric polynomial;integrating;differentiation;matrix;functions cos and sin;differential equation;
URN:	URN:SI:UM:
Type (COBISS):	Undergraduate thesis
Thesis comment:	Univ. v Mariboru, Fak. za naravoslovje in matematiko, Oddelek za matematiko in računalništvo
Pages:	32 f.
Keywords (UDC):	mathematics;natural sciences;naravoslovne vede;matematika;mathematics;matematika;
ID:	19692