[ad_1] 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.…
Read More[ad_1] CHAPTER 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…
Read More[ad_1] 1.1BriefReviewonMathieuequation 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…
Read More[ad_1] TABLE 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…
Read More[ad_1] ABSTRACT 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.…
Read More[ad_1] CHAPTER 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…
Read More[ad_1] CHAPTER 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…
Read More[ad_1] CHAPTER 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…
Read More[ad_1] The 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,…
Read More[ad_1] CHAPTER 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…
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