CHAPTER ONE 1.0 INTRODUCTION Public finance is a field of economics concerned with how government raises money, how that money is spent and the effect of these activities on the economy and on the society. Expenditure…
Read MoreCHAPTER ONE INTRODUCTION 1.1. Background of the study Nigeria is a nation that has been blessed with mineral resources ranging from solid minerals to crude oil deposits; right from the northern part of Nigeria to…
Read More1.1BriefReviewonMathieuequation Mathieu equation isa specialcase of a linear second order homogeneousdifferentialequation(Ruby1995).Theequationwasfirstdiscussedin1868,byEmileLeonardMathieuinconnectionwithproblemofvibrationsinellipticalmembrane.HedevelopedtheleadingtermsoftheseriessolutionknownasMathieufunctionoftheellipticalmembranes.Adecadelater,HeinedefinedtheperiodicMathieuAngularFunctionsofintegerorderasFouriercosineandsineseries;furthermore,withoutevaluatingthecorrespondingcoefficient,Heobtainedatranscendentalequationforcharacteristicnumbersexpressedintermsofinfinitecontinuedfractions;andalsoshowedthatonesetofperiodicfunctionsofintegerordercouldbeinaseriesofBesselfunction(Chaos-CadorandLey-Koo2002).Intheearly1880’s,FloquetwentfurthertopublishatheoryandthusasolutiontotheMathieudifferentialequation;hisworkwasnamedafterhimas,‘Floquet’sTheorem’or‘Floquet’sSolution’.StephensonusedanapproximateMathieuequation,andproved,thatitispossibletostabilizetheupperpositionofarigidpendulumbyvibratingitspivotpointverticallyataspecifichighfrequency.(StépánandInsperger2003).Thereexistsanextensiveliteratureontheseequations;andinparticular,awell-highexhaustivecompendiumwasgivenbyMc-Lachlan(1947).TheMathieufunctionwasfurtherinvestigatedbynumberofresearcherswhofoundaconsiderableamountofmathematicalresultsthatwerecollectedmorethan60yearsagobyMc-Lachlan(Gutiérrez-Vegaaetal2002).Whittakerandotherscientistderivedin1900sderivedthehigher-ordertermsoftheMathieudifferentialequation.AvarietyoftheequationexistintextbookwrittenbyAbramowitzandStegun(1964).Mathieudifferentialequationoccursintwomaincategoriesofphysicalproblems.First,applicationsinvolvingellipticalgeometriessuchas,analysisofvibratingmodes2inellipticmembrane,thepropagatingmodesofellipticpipesandtheoscillationsofwaterinalakeofellipticshape.Mathieuequationarisesafterseparatingthewaveequation using ellipticcoordinates.Secondly,problemsinvolving periodicmotionexamplesare,thetrajectoryofan electron in aperiodicarrayofatoms,themechanicsofthequantumpendulumandtheoscillationoffloatingvessels.ThecanonicalformfortheMathieudifferentialequationisgivenby+ y =0, (1.1)dy 2dx2 [a-2qcos(2x)](x)whereaandqarerealconstantsknownasthecharacteristicvalueandparameterrespectively.Closely related to the Mathieu differentialequation is the Modified Mathieudifferentialequationgivenby:- y =0, (1.2)dy 2du2…
Read MoreTABLE OF CONTENTS Title page Declaration Certification Dedication Acknowledgement Table of Contents Abstracts CHAPTER ONE: INTRODUCTION 1.0 Introduction 1.1 Historical Background of the Study 1.2 Aims of the Study 1.3 Objectives of the Study 1.4 …
Read MoreABSTRACT It is widely accepted that water supply will be a pressing issue in this century. Thus, position of adequate rainfall in the development of human and natural resources is a worthwhile research work. The…
Read MoreCHAPTER ONE 1.1. INTRODUCTION Vaccination of dogs generally is of utmost importance to us seeing that dog is man’s best friend. Vaccinating dogs not only helps to save dogs from infections but it also helps…
Read MoreCHAPTER ONE 1.1. INTRODUCTION Vaccination of dogs generally is of utmost importance to us seeing that dog is man’s best friend. Vaccinating dogs not only helps to save dogs from infections but it also helps…
Read MoreThe introduction and development of the notion of a matrix and the subject of linear algebra followed the development of determinants, which arose from the study of coefficients of systems of linear equations. Leibnitz, one…
Read MoreCHAPTER ONE 1.1 INTRODUCTION From the beginning of time man has been interested in the rate at which physical and non physical things change. Astronomers, physicists, chemists, engineers, business enterprises and industries strive to have…
Read MoreCHAPTER ONE 1.1 INTRODUCTION The increasing desire of the government and civilization to improve the maintenance of law and order and to engage in crime prevention, has led to the search for data on all…
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