Elementární metody řešení diferenčních rovnic

Abstract

Nazev prace: Eleinentanii melody fcseni diferencnieh rovnic Autor: Antonin Sadil Katedra (ustav): Katedra matematieke analyzy Vcdonci bakalafske prace: RNDr. Robert Corny,Ph.D. e-mail vedouciho: rc.erny^karlm.mff.eimi.e/ Abstrakl: Tato prace pojednava o metodaeh feseni linearnich diferencnieli rovnic. Zamefuje se na. vlastnosti feseni homogomn'ch rovnic a nalezeni fundamentalniho systemu pro jodnodnoho, nasobne i komplexni kofeny charakteristickeho polynomu. U nchomogcnnich rovnic sc pak zamefuje pfedevsim na inctody pro nalezeni partiku- larniho feseni. Dale so kratco zal">yva fosenim linoarni diferencni rovnice prvniho fadu s nekonstaiiUiimi kooficienty a v zaveru popisuje uietody feseni sonstav liiioarnich diforencnich rovnic prvniho radii. Cola toorie jo poistavona na dnkazoch a pro lopsi pochopeni je proloiona nekolika ilustrativnimi pfiklady. Klicova slova: homogenni rovnice, nohoniogonni rovnice, fundainentalni system Title: Elementary methods for solution to difference equations Author: Antonin Sadil Department: Department of Mathematical Analysis Supervisor: RNDr. Robert Ceriiy,Ph.D. Supervisor's e-mail address: rrerny^karlin.mfT.cuni.cz Abstract: This work presents aboul methods for solution to difference equations, ft focus on characteristics of solutions of the homogeneous equations and finding...

Nazev prace: Eleinentanii melody fcseni diferencnieh rovnic Autor: Antonin Sadil Katedra (ustav): Katedra matematieke analyzy Vcdonci bakalafske prace: RNDr. Robert Corny,Ph.D. e-mail vedouciho: rc.erny^karlm.mff.eimi.e/ Abstrakl: Tato prace pojednava o metodaeh feseni linearnich diferencnieli rovnic. Zamefuje se na. vlastnosti feseni homogomn'ch rovnic a nalezeni fundamentalniho systemu pro jodnodnoho, nasobne i komplexni kofeny charakteristickeho polynomu. U nchomogcnnich rovnic sc pak zamefuje pfedevsim na inctody pro nalezeni partiku- larniho feseni. Dale so kratco zal">yva fosenim linoarni diferencni rovnice prvniho fadu s nekonstaiiUiimi kooficienty a v zaveru popisuje uietody feseni sonstav liiioarnich diforencnich rovnic prvniho radii. Cola toorie jo poistavona na dnkazoch a pro lopsi pochopeni je proloiona nekolika ilustrativnimi pfiklady. Klicova slova: homogenni rovnice, nohoniogonni rovnice, fundainentalni system Title: Elementary methods for solution to difference equations Author: Antonin Sadil Department: Department of Mathematical Analysis Supervisor: RNDr. Robert Ceriiy,Ph.D. Supervisor's e-mail address: rrerny^karlin.mfT.cuni.cz Abstract: This work presents aboul methods for solution to difference equations, ft focus on characteristics of solutions of the homogeneous equations and finding...